precalculus

[trim fable]

oh well

ill just do this tom

so cya 😛

[clever inlet]

cya

[trim fable]

or later idk

[viscid thistle]

how do I find the maximum and minimum of y=sinx+sin2x

[willow bear]

what have you tried and where are you stuck

[viscid thistle]

ok

I tried adding the amplitudes of both

didnt work

factoring out sin doesnt work since it changes the equation

and it's the last problem on my math homework

and I wanna go play CSGO

[willow bear]

hang on. given that you're posting this in #precalculus rather than #calculus, i suppose you're not supposed to use derivatives

is that correct

[viscid thistle]

yyea

im in precalc

derivative isnt that just slope or seomthing

[willow bear]

forget it

[viscid thistle]

iidk I take calculus next year

[willow bear]

why not use a sum to product identity then

[viscid thistle]

what

is that

u mean sum and difference forumula?

[willow bear]

https://www.cliffsnotes.com/study-guides/trigonometry/trigonometric-identities/product-sum-and-sum-product-identities

$\sin(x) + \sin(2x) = 2\sin(\frac32x) \cos(\frac12x)$

[obsidian monolith]

Ann:

[viscid thistle]

so it is 2

[willow bear]

maybe

[viscid thistle]

0.o maybe

[willow bear]

the maximum value cannot be greater than 2

[viscid thistle]

why

ohbyea the amplitute XD

[willow bear]

because sin and cos are both bounded by 1

so $2\sin(...)\cos(...) \leq 2$ no matter what the contents of those sin and cos are

[obsidian monolith]

Ann:

[willow bear]

if it so happens that there exists a point for which 2sin(3x/2)cos(x/2) is equal to exactly 2, then congratulations, that's your maximum value

[viscid thistle]

nani

ur math seems confusing

[willow bear]

what part of what i said is confusing?

[viscid thistle]

bounded by 1

I know the range is only 1

[lilac pier]

Ann may I say something

[willow bear]

i'm saying $\sin(t) \leq 1$ and $\cos(t) \leq 1$ for all $t$ @viscid thistle

[obsidian monolith]

Ann:

[willow bear]

@lilac pier what

[viscid thistle]

ok

I know thatt

[lilac pier]

nvm

[viscid thistle]

by how is sin(...)cos(...) less than or equal to 2

[willow bear]

no

did you read what i said

$2\sin(...)\cos(...) \leq 2$

[obsidian monolith]

Ann:

[willow bear]

$2\sin(...)\cos(...) \leq 2 \times 1 \times 1$

[obsidian monolith]

Ann:

[viscid thistle]

OH SHIT

2 times 1

times 1

ARITHMATIC

[willow bear]

ftr, it doesn't look like this is gonna be enough to find the actual max value

[viscid thistle]

what do I do now

😦

so I don't do my hw?

[willow bear]

i don't see a way to do this without calculus

here's the desmos graph

[viscid thistle]

😦

what if I use sum and dufference formula

sin(x+2x)

[willow bear]

uh what

you don't have sin(3x)

[viscid thistle]

and like sinxcos2x+cosxsin2x

[willow bear]

you have sin(x) + sin(2x)

no

[viscid thistle]

and like graph it

[willow bear]

you are not starting with sin(x+2x)

sin(x) + sin(2x) is not the same thing as sin(x + 2x)

[viscid thistle]

I know

wait

[willow bear]

starting with sin(3x) is going to be pointless

[viscid thistle]

I saw my teacher do sin+cossin=sin(1+cos)

[willow bear]

sin(x) + cos(x)sin(x) = sin(x) * (1 + cos(x)) sure

[viscid thistle]

why

is it cause there's no variable

and it

[willow bear]

why what

$a + ab = a(1+b)$, this is just algebra and has nothing whatsoever to do with trig

[obsidian monolith]

Ann:

[viscid thistle]

I know

I'm not stupid I'm just uhh

Are you finding min/max?

fuck blame it on the sprite

yes sir

Hmm

@willow bear

I think knight has a soluuttion

And I’m assuming you don’t know calculus?

yyep

how'd u know ❤️

Hm

calculalusssss

my precalc book is shit

utter garbage

[lilac pier]

Well

[viscid thistle]

no I'm a human

not a well

lol best math teachers

[willow bear]

...

[lilac pier]

Since y=sinx and y=sin2x have a phase difference, we can't add 1+1.

[willow bear]

what

[viscid thistle]

explaining calculus without calculus

[willow bear]

they don't have a fucking phase difference

they're not phase-shifted wrt one another sup

[viscid thistle]

0.o oh damn

[lilac pier]

They are?

[willow bear]

no they're not

[viscid thistle]

theyy dont

[willow bear]

they're fucking sin(x) and sin(2x)

[viscid thistle]

even i know that

[willow bear]

they have fucking DIFFERENT FREQUENCIES

[viscid thistle]

OH DAMN

U PULLED OUT THE F WORD

[lilac pier]

oh right I meant that then

no it's okay she is the master

[willow bear]

sup just don't spew more nonsense aobut things you know nothing about

just stop

[viscid thistle]

0.o

[lilac pier]

Yeah my bad

[viscid thistle]

What’s the point of analyzing them separately

so do what do I do now

[willow bear]

honestly i don't know

[viscid thistle]

😢

[willow bear]

this problem is inaccessible at your level. i really doubt that there's a way around it.

[viscid thistle]

u think it wants me to graph it and wright down what I see

[willow bear]

here i can even give the exact answer

which i guarantee you is impossible to arrive at w/o calculus

[viscid thistle]

1.76 or something

[willow bear]

it's 1.76ish yes but unless you're asked to find that value to two decimal places this won't do

[viscid thistle]

How would I do it with calculus>

??*

Do you know anything about derivatives

[willow bear]

he does not

[viscid thistle]

its the slope or something

like y=5x has a derivative of 5

[willow bear]

i'm not about to give a calculus 1 lecture in ten minutes

it's more than just "the slope or something"

[viscid thistle]

I mean real genius can explain anyyhting in 10mins

[willow bear]

no

[viscid thistle]

I don’t think there’s a point for you to understand the calculus right now

😦

[willow bear]

you can't explain a phd thesis in 10 minutes in its entirety to a five year old

[viscid thistle]

I'm 16

rUdE XD

[willow bear]

i was not referring to you specifically

nor was i likening myself to a phd, which i'm not

[viscid thistle]

yes ma'am

[willow bear]

the exact answer is $\frac{(3 + \sqrt{33})\sqrt{30 + 2\sqrt{33}}}{32}$, and you'd find that by setting $\dv{x} (\sin(x) + \sin(2x)) = 0$ and evaluating $\sin(x) + \sin(2x)$ at those values of $x$.

[obsidian monolith]

Ann:

[viscid thistle]

The metaphor is you can’t explain something a little more advanced to a beginner without providing more background

And that background will be given to you in further courses

my precalc class supposed to be like around half a semester long

[willow bear]

uh yeah you were given a calculus problem in a precalc worksheet and you don't have the tools necessary to solve it

there really is nothing else to be said here lol

[viscid thistle]

it's not in a worksheet

it's in my book

[willow bear]

homework assignment

whatever

[viscid thistle]

my book is stupid

??

[willow bear]

idk why anyone would even put that in a precalc book

¯_(ツ)_/¯

[fluid shore]

Uh can you show us the question from the book

[viscid thistle]

Precalculus 5th edition

mathematics for calculus

65

[fluid shore]

,rotate 270

Wow fk

[native sequoia]

yeah it has that graph symbol

[viscid thistle]

what's that mean

[dim jungle]

just say ur pencil wrote it and ur brain agreed

[fluid shore]

You gotta graph it to get the maximum and minimum

[viscid thistle]

with hand

or calculator

Calc

cause idk hwo to graph this by hand

[fluid shore]

Even if it was with a calculator, do it by hand

It's better for you

[viscid thistle]

@willow bear how do i do it by hand

[dim jungle]

just draw

squiggles

but then

like rly close

but then

make it so that one little box is like 1000 pi

so they cant say ur wrong

[willow bear]

you can't

[dim jungle]

its just a lot of squiggles mushedtogether which lookes like ||||

[willow bear]

what does that graph icon next to the question mean

[viscid thistle]

Yes but the range really matters with this

idk

[fluid shore]

It just means you have to get it by graphing it. Typically, it means you have to use some gdc

Looking at the rest of the questions, they don't seem to lend themselves to precalc methods. You probably have to use a gdc to graph them and get the maximum

[viscid thistle]

Idk

I think I need to use a graphing calculator

[willow bear]

it says it right there

[viscid thistle]

0.o

[willow bear]

if only you just

read the paragraph

titled "Scientific and Graphing Calculators"

[viscid thistle]

we just got this book

[willow bear]

read it

[fluid shore]

:/

[viscid thistle]

all of it?

[willow bear]

it ain't that much

[fluid shore]

That entire conversation above took place for absolutely nothing

[willow bear]

unless your reading comprehension only allows you to grapple with about a dozen words at a time

[viscid thistle]

bruh why u roast me like that

[fluid shore]

It's not a roast

[viscid thistle]

kinda is

[dim jungle]

it looks like a thick book

tho

[fluid shore]

Dude

[viscid thistle]

it is thick

[fluid shore]

If it doesn't apply to you, it's not a roast.

[willow bear]

how hard can it be to read ONE (1) paragraph containing PRECISELY the information you need

[viscid thistle]

thicker than me

I read it now

[willow bear]

yeah great

[viscid thistle]

I dont wnna read the rest tho

XD

[dim jungle]

bad

go read

[viscid thistle]

these symbols are trippy

[willow bear]

can you now

tell me what the graph icon means

based on what you read

[viscid thistle]

use a graphing calculator

those are expensive

😢

[dim jungle]

online

graphing calc

[viscid thistle]

Desmos is great

I mean I have one

[fluid shore]

I think some people use desmos or something

[willow bear]

a graphing calculator or a computer with graphing software.

[viscid thistle]

I'm just saying it's expensive

[willow bear]

READING COMPREHENSION BRUH

[viscid thistle]

If you have one use it to your advantage

[dim jungle]

this man has the biggest brain

[viscid thistle]

I did better on the math sat part

[willow bear]

YA GOTTA GET SOME AT SIXTEEN YEARS OF AGE DONTCHA THINK

[fluid shore]

I can agree with you: they're really expensive and very dumb

[viscid thistle]

english is hard

[dim jungle]

yeah english is hard

[viscid thistle]

ann r u 30?

[fluid shore]

Ann, he didn't say he couldn't use an online software.

[willow bear]

20

[viscid thistle]

0.o do u atten uni

for math

[willow bear]

yes

i'm in my third year

[viscid thistle]

is it a top uni?

[willow bear]

i think so

[viscid thistle]

harvard?

[willow bear]

no

[viscid thistle]

yale?

[willow bear]

i'm not in the US

nor in an english-speaking country

[viscid thistle]

Vietnam?

[willow bear]

lmao

but no

[viscid thistle]

is it in asai?

[willow bear]

no

[viscid thistle]

Asia*

[dim jungle]

is it in europe

[viscid thistle]

uhh poland?

[willow bear]

closer but no

[viscid thistle]

hungary?

[willow bear]

no

[viscid thistle]

Germany?

[willow bear]

saint petersburg state university, in russia

[fluid shore]

Lmao

[viscid thistle]

RUSKY

Privet moy drug

[willow bear]

....

[dim jungle]

very nice

[viscid thistle]

Piveat

Kak dela

[dim jungle]

how much work

do u get

[willow bear]

"piveat"

[viscid thistle]

moyo emya jager

[dim jungle]

like how many hours a day

[viscid thistle]

priveat*

XD

[dim jungle]

hw

[willow bear]

ok uh

[dim jungle]

avg

[viscid thistle]

Skoko vremine u vas?

[fluid shore]

Take this to chill

[willow bear]

can we like not do poorly transcribed russian

[viscid thistle]

I like russia

[willow bear]

also yeah

[viscid thistle]

it has snow 😄

[fluid shore]

Take this conversation to chill, guys

[willow bear]

this is #chill conversation now

[dim jungle]

im guessing like 3 hours

a day?

hw?

[viscid thistle]

I can speak, can’t read/write );

[dim jungle]

no thats too little

[viscid thistle]

lol

[fluid shore]

TAKE THIS CONVERSATION TO CHILL

[viscid thistle]

ttatt wont work

[dim jungle]

maybe 5 hours?

[viscid thistle]

OK LEMME BRING IT BACK TO MATH

what's the arc length of the curve in p

p is russia

cause priveat

[dim jungle]

no ones going to respond

[viscid thistle]

What

[fluid shore]

TAKE THIS CONVERSATION TO CHILL

[viscid thistle]

and russia in russain starts with p

Россия

[fluid shore]

Stop. Others might want to ask questions here. Go to #chill

[native sequoia]

pootis

[summer monolith]

Another misprint?

[fluid shore]

Nope

$-ct = \ln(\frac{B}{cD}) \implies t = -\frac{1}{c} \cdot \ln(\frac{B}{cD}) = \frac{1}{c} \cdot \ln(\frac{cD}{B})$

[obsidian monolith]

Abhijeet Vats:

[fluid shore]

There we go

basically, the stuff inside the logarithm was flipped

@summer monolith

[summer monolith]

ln(B/cD)=-ln(cD/B) ?

[languid crane]

log properties

[fluid shore]

mmmh that was the property that was used

[summer monolith]

log properties
Can't see this one in the list

[uncut mulch]

$-\ln(x) = \ln(x^{-1}) = \ln ( \frac 1x )$

[obsidian monolith]

ramonov:

[uncut mulch]

application of power rule

[fluid shore]

what do you mean you 'can't see this one in the list'

you don't just have a piece of paper listing all the laws that you've encountered so that you can just pull one or two laws from it when you need them

try to actually follow the logic of the argument and you'll live a happier life

[languid crane]

its clearly there

log_a (x^n) = n log_a(x)

no?

[fluid shore]

NO, THIS IS WHAT I MEAN

DO NOT SIMPLY HAVE A LIST THAT YOU'RE TAKING FORMULAS OFF OF.

[summer monolith]

Is this an imperative or a statement?

And why not?

It makes life easier

Wew
I didn't realize that 1/(a/b)=b/a

Not sure though. I need to check again.

[fluid shore]

??????????

[summer monolith]

Nevermind
I was just thinking about the derivative of ln(cD/B)

[summer monolith]

Lol
I've just waisted hafl an hour trying to comprehend how c^2De^-ct derives from 1/c*ln(cD/B)

[stuck lark]

$\dv{S}{t}=B-cDe^{-ct}\\\dv[2]{S}{t}=\dv{t}(B-cDe^{-ct})=,?$

[obsidian monolith]

RokettoJanpu:

[summer monolith]

I did realize what was the problem

eventually

[stuck lark]

👍🏾

[nova dew]

$\lim_{x\to 1} \frac{x^m - 1}{x^n -1}$ hello I'd appreciate some help

[obsidian monolith]

CoolShot:

[nova dew]

what am I supposed to do exactly

[fluid shore]

Find the limit, if it exists

[willow bear]

one of the few cases where LH makes it possible to avoid having a shitton of different cases

[undone pawn]

wdym different cases?

[willow bear]

natural, integer, rational, arbitrary real

[undone pawn]

ohh ok

[pale bison]

wait you're learning derivative but don't know log rules what

[fluid shore]

?

The basic idea of a derivative has nothing to do with log rules

[pale bison]

i mean... isn't log a prereq of calc

oh nvm this is precal, ok

[fluid shore]

I mean, i guess it is but it is not a prerequisite to understanding the basic idea of a derivative or an integral

[trim fable]

how would u do the graph on the right?

f(g(x))

how would i fine the points for that?

or find the equation?

can anyone help with that

oof

[fluid shore]

Well, what do you think?

You're trying to find f(g(x)), where the input is now g(x), rather than x

What can you do with that?

[trim fable]

oh

uh

idk ;-;

I do this?

is there an easier way tho :c

well faster*

@fluid shore

[fluid shore]

Well, how's that gonna help you here, though?

[trim fable]

oh is it not?

[fluid shore]

When you suggest a method of doing something, you need to consider the reasons for why it's gonna help you.

[trim fable]

uh u can

[fluid shore]

Did i say it wouldn't? I'm asking ya to think through it and see if it does help you.

[trim fable]

find the points for f(g(x))

then plot them

using that^

[fluid shore]

Well, you could do that, certainly

Since f(g(x)) = 2g(x) + 1 = 2(3x-2) + 1 = 6x - 3, you can also do it that way.

[trim fable]

oh then

simplify?

after making them equal?

so x-3?

@fluid shore

would be

f(g(x)) ?

[fluid shore]

No

[trim fable]

oh

[fluid shore]

I just found f(g(x)) for you

[trim fable]

oof

oops

oh so

u plugged g(x) into

the f(x) equation?

[fluid shore]

Yes

[trim fable]

oh

ok

[fluid shore]

Keep in mind, the input has now changed from being x to g(x) instead.

[trim fable]

oh ok

so it would be 6x-3?

OH yay

thats what u got

so that would be the function for f(g(x))

so i could just plot it?

[fluid shore]

What do you think?

[trim fable]

question tho how does this relate to the mapping thing?

i think : yes

but i dont really understand why we do this

can u explain how they are related or something

😛

[fluid shore]

What do you mean

[trim fable]

nvm

lol

what is that asking

[fluid shore]

Well, i mean, there's a bit of work that does go into all of this

[trim fable]

ye

slope is 6 equation is 6x-3

[fluid shore]

There's a bit of theory so you'll just have to read up on it. Then, you can ask questions if you're confused.

[trim fable]

but what about the next part

is that what I just did?

[fluid shore]

Yes

[trim fable]

oh

[fluid shore]

Lol

[trim fable]

and the next thing?

[fluid shore]

That last bit?

[trim fable]

yes

[fluid shore]

They're asking you to compare g(f(x)) with f(g(x))

[trim fable]

question th

u know when they asked to graph

was i expected to just do it without

solving for it?

[fluid shore]

Well, i think that's what you were meant to do

You were supposed to plot points

[trim fable]

ok

uh

for the last bit

is the answer no

coz its not the same equation?

@fluid shore

[fluid shore]

Idk, you tell me

[trim fable]

yes

its not

[fluid shore]

Yeap, so if they don't give the same result, they're not the same

[trim fable]

Yay

im self teaching myself this

before school starts which is why im so clueless LOL

u know whats sad

i did what u taught me

i got

x^2+2x+1

but sadly i forgot how to Graph quadratics thats super sad

@fluid shore

lol

oh wait

i can complete the square

but i think i forgot how to

rip

@fluid shore Am i doing it right so far tho?

[fluid shore]

Lmao

[trim fable]

lol

[fluid shore]

f(g(x)) = (g(x))^2 = (x+1)^2

[trim fable]

yes

i expanded.. oof

was i not

supposed to

😅

lol

[fluid shore]

No, you asked about completing the square

[trim fable]

oh

[fluid shore]

That's the completed square

[trim fable]

thats literally what i

started with tho..

[fluid shore]

First of all, graph x^2 and x+1

[trim fable]

i did

[fluid shore]

Then, graph (x+1)^2 by plotting points

[trim fable]

ok

[fluid shore]

Legit, if you're not confident about doing it straight away, just plot points

There's nothing harmful about that

[trim fable]

okk

hmm

is it the same graph

no right?

wait tbh for

i think they are does it count if

actually nvm

they aren't lol

right?

@fluid shore

[fluid shore]

What

You mean is (x+1)^2 the same as x^2

No they are not the same, my dear

But

They do look the same cos they're both parabolas

[trim fable]

yes

lol

ok so

i did this part on my own

and other points I got were

using g(1) point (1,4)
using g(2) point (2,9)
using g(-1) point (-1,0)

are those right

@fluid shore

[fluid shore]

Do you expect me to do the calculations in my head?

[trim fable]

yeahh 😛

ur smartt lol

[fluid shore]

Check the calculations you have done. If they're correct, then they're correct. If they're not, redo them.

Then, plot the points.

[trim fable]

uh how do i check if they are

oh

plug them

[fluid shore]

Did you follow the steps given correctly? Did you find every value that you need to calculate correctly?

[trim fable]

into the equation

yes

i think im right

[fluid shore]

Yes.

[trim fable]

waitttt

x^2 is equal to

(x+1)^2

its the same graph

but translated

so they are equal? @fluid shore

[fluid shore]

???????????????

They look the same, yes

As i said before, they're both parabolas

[pale bison]

they're not equal

[trim fable]

why?

[fluid shore]

Is 4^2 = 3^2?

[trim fable]

but its the same

graph just

translated?

soo

does that

not count?

[pale bison]

shifted

[trim fable]

yes

[fluid shore]

Yes, they look the same. They're both parabolas

[pale bison]

Is 4^2 = 3^2?
answer this

[trim fable]

lol

16=9

yes

jk

ok

😛

[fluid shore]

Okay, so have you solved the problem?

[trim fable]

yup

😄

[fluid shore]

Good.

[trim fable]

yes

ima teach myself lesson 2 now

LOL

[pale bison]

have fun and feel free to ask questions

[trim fable]

I prob will

ask

LOL

i self teaching which does't help when ur just answering questions from class notes which u would do with the teacher but

annywayssss

i wanna get ahead so i can stay in winter break mode when school starts LOL

coz ill be done the work 😄

[fluid shore]

ill be done the work

Consider taking some English classes as well 🙂

Prank

[pale bison]

ah yes

lmao

[trim fable]

what do u mean

i have english next semester sooooo

[fluid shore]

Are you in high school?

[trim fable]

yeah

im in grade 12

lol

[pale bison]

cool beans

[trim fable]

I need a uniiiiiiiiii

ahhhhh

im scared tho

all my marks have been dropping

;c

[pale bison]

like unicycle? everyone is scared of a unicycle, you're not alone

jokes aside, just have a positive attitude and roll with it know what i mean

[trim fable]

LOL

nah I mean university 😛

[pale bison]

yeah ik

[trim fable]

ik 😛

[fluid shore]

What do you want to study in uni?

[trim fable]

Engineering

or computer science

i would honestly just do math but apparently u cant really do much with just math so rip

are u guys american?

[fluid shore]

I'm Singaporean. I believe Publius is American.

[pale bison]

yes

[trim fable]

ur from Singapore?

oh ok

OK TIME FOR THE NEXT LESSON

😛

ok then i guess im

doing that

isn't that what we were doing

@fluid shore

making them equal?

[arctic mantle]

Halp <@&286206848099549185>

[trim fable]

?

oh that

i think i forgot how to rip

;-;

@pale bison uh u know how

it says solve

does that mean

[pale bison]

[trim fable]

for the first one

oh

what did i do ;-;

[pale bison]

that's meant for MrBioFex

[trim fable]

oh ok

(x+3) (x^2-12) for i
then would ii be (x^2-12) (x+3)?

[clever inlet]

How'd you get that

[trim fable]

f(x) x g(x)

[clever inlet]

It's composition

Not multiplication

[pale bison]

they're not multiplying

the key word is composition like Kangaroux said

[trim fable]

oh

idk then ;c

self teachings so hard ahh

[pale bison]

okay

i'll give you one quick example

[trim fable]

OH OK

yay

[pale bison]

say you have $f(x)=x^2+2x$ and $g(x) = \sqrt{x}$

[obsidian monolith]

Publius:

[trim fable]

ok

😮

[pale bison]

then, when you say f compose g, what that means is that:

take the function g(x), and plug it into f(x)

so, you have f(g(x))

[trim fable]

oh

wait

so the circle means

composite?

[pale bison]

so, whenever you see x in the function f(x), you replace it with g(x)

yes, that circle

exactly

[trim fable]

oh..

that makes so much sense

i thought the circle was

multiplication coz sometimes a dot represents that

[pale bison]

multiplication is mostly likely a dot

[trim fable]

ye

[pale bison]

only losers use X

[trim fable]

lol

😛

[fleet yew]

Its not X

[trim fable]

lol

[fleet yew]

Its ×

[trim fable]

lol

[pale bison]

ok

ok you have a macro or greek letter keyboard or whatever

[fleet yew]

I personally like the cross notation

It reflects the true meaning of multiplication

[trim fable]

hmm

i use both

depends on my mood

lol

[pale bison]

the true meaning of multiplication is to expand it to addition

[fleet yew]

To multiply a and b means to find the area of a rectangle with side lengths a and b

[trim fable]

question

[fleet yew]

Kind of like "crossing" the side lengths if you will

[trim fable]

so from the notes i sent

f composite of g(x)

for a is

x^2 -12 +3 ?

[fleet yew]

x^2-12+3=x^2-9

[trim fable]

x+3
(x^2-12) +3
x^2 -12+3

?

[fleet yew]

Yes

Combine like terms

[trim fable]

oh

oops

lol

didn't realize that

thankss

[fleet yew]

Lol this is what precalc is nowadays?

[trim fable]

then

oh this is

unit 9

last one

[fleet yew]

Im just old ig

[trim fable]

oh

[fleet yew]

I dont remember precalc

I just recall it being way harder

[trim fable]

lol

[fluid shore]

It matters not how hard it is. It only matters that you understand what's being presented.

[trim fable]

tho I HAVE TIME

wellllllllll

uniiiii caressssssss

about the markkkkk

;c

which hurts but its fine..

[pale bison]

this pre uni section of discord is really mixed up

[trim fable]

what do u mean?

[fluid shore]

Yer mum was mixed up

PRANK

RELAX

MEMES

CHILL

SHHHHh

[trim fable]

huh

[pale bison]

well, because they're all "basic" and i don't think it matters that much that we have four different channels for it

[trim fable]

so g composite of f is x^2 +6x -3?

[pale bison]

@fluid shore thanks good meme

i'm reporting you to the mod

enjoy your ban

[fluid shore]

Nah 4 different channels is so that we can help different people with different questions

😦

[pale bison]

jk

[trim fable]

hey so was i right

AHH

[pale bison]

which one are you talking about?

[trim fable]

a

for ii

and iii is just saying if both equations were equal right?

so no?

[pale bison]

yes you are correct that "so g composite of f is x^2 +6x -3" for a)

[trim fable]

OK

yay

also was that what iii wants^^

[pale bison]

i think there's a typo

[trim fable]

ye

same

do they mean

f o g(x) = g o f(x)?

[pale bison]

yees

[trim fable]

answer = no

😛 ?

right 😛

[pale bison]

what's your reasoning?

[trim fable]

coz they aren't the

same equation

[pale bison]

hmm

if i have f(x) = x+1 and g(x)=x-1
then f compose g and g compose f are the same, despite them being different

[trim fable]

huh

[pale bison]

so them being different is NOT enough to finish the problem

[trim fable]

im so confused now ;-;

[pale bison]

do the dirty work and calculate it

[trim fable]

how

[pale bison]

just like how you did in question i

[trim fable]

oh..

[pale bison]

do f compose g, then do g compose f

then compare them

[trim fable]

i did tho

[pale bison]

okay, then good, that's the right way to do it

[trim fable]

x^2-9 = x^2+6x-3

and they aren't

equal

[pale bison]

where did those equations came from?

[trim fable]

f composite of g(x)

and then g composite of f(x)

i jus used my answers for i and ii for iii

can I not?

[pale bison]

ohh

i read the question wrong

i thought i is for a)

ii is for b

and iii is for c

my bad, yes

you're right

[trim fable]

lol

ok

so i just look if

they are the same

[pale bison]

yeah

[trim fable]

and say yes or no

ok lol

u really made that

complicated thats

very funny 😛

lol

[pale bison]

... okay

[trim fable]

LOL

aww sorry

did i hurt ur feelings ;-;

[pale bison]

my bad

no you didn't i have no feelings

[trim fable]

question are u in uni

aww why not

[pale bison]

yes

[trim fable]

oh wow

what year

😮

[pale bison]

2nd

[trim fable]

oh 😮

cool

hows

that going

[pale bison]

so far so good
but then i compare my self to people here and i feel like i'm a big dumb

[trim fable]

oh rip

honestly idk if im dumb or smart

coz im good at math but lol sometimes Im just

very stupid

[pale bison]

always happens, to anyone

[trim fable]

my marks dont show that im good at it ;-;

it did before

which is why i dont find marks a fair way to

judge someones intelligence

coz i was at a 87 now look im at a 77

CAUSE: STRESS DURING TESTS

[pale bison]

well, test scores don't measure intelligences first of all

[trim fable]

well averages?

coz i think i should be at a 87 tbh

maybe even 90

[pale bison]

it measures how well you understood the concepts (at least it tries to)

[trim fable]

i could have gotten there

if i didn't mess up so bad

[pale bison]

and that corresponds to how much you practice

more practice = higher score

[trim fable]

one test brought me down 7%

[pale bison]

so just work on it

[trim fable]

then i dropped 1 each time lol

but i do tryyyy

i do practice i just

stress out during tests and i blank out coz all thats in my mind is u gotta do this if u wanna go to uni and then

i panic when i dont get something then my confidence goes ⬇️

[pale bison]

well yeah, that happens

[trim fable]

but does uni care

NOPE

im scared ;c

lol

hey so for

b

i would be x+2

and ii would be x

right?

[willow bear]

how did you get x+2 in b/i

[trim fable]

oh ok so

(square root of x+1)^2 +1

the square cancels the square root

so then

x+1+1

which equals x+2

right?

[willow bear]

alright first off

don't write square root like that

second, $g(x)$ is not $\sqrt{x+1}$

[trim fable]

like what?

[obsidian monolith]

Ann:

[trim fable]

it was -1 actually

oh rip

OOPS

[willow bear]

third, you really should write sqrt(x-1)

[trim fable]

oh ok

[willow bear]

f(g(x)) = (sqrt(x-1))^2 + 1

[trim fable]

wellits hard to say what u wanna say

[willow bear]

with the parentheses

[trim fable]

for math on

messages

its right on my paper

LOL

oh btw the answer should be x

these equations are equal YAY

[willow bear]

b/ii is not x, ftr

[trim fable]

oh rip

i plugged in +1.. again..

🤦‍♀️

would it be

x- sqrt(2)

@willow bear

[willow bear]

would what be x - sqrt(2)?

[trim fable]

the answer for b/ii

[willow bear]

no

[trim fable]

oof

what did i do wrong ;-;

[willow bear]

well show your work

[trim fable]

ok

[willow bear]

on paper maybe

so that the communication mishap doesn't happen again

[trim fable]

sqrt(x-1)
sqrt(x^2-1-1)
sqrt(x^2-2)
cancelled square with square root for x which gave me:
x- sqrt(2)

[willow bear]

okay so

first off

f(x) is not x^2 - 1

and second

not only is sqrt(x^2) not equal to x in general, you also pulled a fucking freshman's dream

[trim fable]

oooooooof

OMG

why am i copying these wrong

LOL

wait no

wait ye

rip

hey so i was

right before

it was x?

[willow bear]

no you weren't

[trim fable]

sqrt(x^2)

is x

[willow bear]

$\sqrt{x^2} = x$ is not true in general!

[obsidian monolith]

Ann:

[trim fable]

but the

square was

outside

oh no

nvm

rip

thanks

[willow bear]

if $x = -5$, then what is $\sqrt{x^2}$?

[obsidian monolith]

Ann:

[trim fable]

5

[willow bear]

exactly.

[trim fable]

true

ok

my bad i thought it was outside coz

idk

lol

no wait i messed up

i guess i just did it without actually considering where the square was

so the final answer is just sqrt(x^2)

or i can fo

cant i do

x^(2 x 1/2)

and i get x^(2/2)

which is just x?

@willow bear

[willow bear]

no! that only works if x is positive! which you cannot assume!

[trim fable]

oh

[willow bear]

you literally just demonstrated that $\sqrt{x^2}=x$ is false in general, since for example it is false for $x=-5$ !

[obsidian monolith]

Ann:

[trim fable]

lol

oops

[willow bear]

think! think about the things you say!

[trim fable]

;-;

sorry ;-;

so the answer is just

sqrt(x^2)

[willow bear]

sqrt(x^2) can be simplified.

not to x, but to something else.

[trim fable]

to?

oh

(x^2)^1/2 ?

[willow bear]

no

|x|

[trim fable]

oh..?

how so

[pale bison]

$x^{2^\frac{1}{2}}=\sqrt{x^2}=|x|$

[obsidian monolith]

Publius:

[trim fable]

but how is it the

absolute value?

[pale bison]

well

take -4 for example

[trim fable]

ok

[pale bison]

square that number

[trim fable]

oh..

i get it ok

[pale bison]

neat

[trim fable]

u will always square the

number so

[uncut mulch]

bad tex

[trim fable]

the - will always become

a positive right?

so then u dont have to deal with

square rooting a negative number?

which is why it will be

absolute?

coz then u get the same number

[pale bison]

umm

[trim fable]

but positive since u square then cancel that with the square root

[pale bison]

square root of a negative number is called imagenary

[trim fable]

but the square will convert to a positive then undo

yes

ik