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[ruby wedge]

How to find domain algebraicly?

[umbral sphinx]

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[copper marlin]

do u know

what a

domain is

@ruby wedge say quickly pls

i can explain it

if u want

[ruby wedge]

domain is all the x values

but

i figured that out

but

how to find range

[copper marlin]

yep domain maps to the co domain

[ruby wedge]

how to find range algebracily

[copper marlin]

sure

lets do it

first step

try

taking the x

to one side

[copper marlin]

u can do it here by

[ruby wedge]

y= 1/(x^2 - 5x + 6), make x the subject?

[copper marlin]

$(x^{2}-5x+6)*f(x)=1$

[modern solstice]

Gary

[copper marlin]

do the multiplication now

open up brackets

[ruby wedge]

yx^2 - 5xy + 6y = 1

[copper marlin]

$x^{2}f(x)-5xf(x)+6f(x)=1$

yep

now

[modern solstice]

Gary

[copper marlin]

take the 1 to the left too

$x^{2}f(x)-5xf(x)+6f(x) -1 = 0$

[modern solstice]

Gary

[copper marlin]

thats quadratic

u see

[ruby wedge]

ye

[copper marlin]

u know like

$D= \sqrt{b^2 - 4ac}$

[modern solstice]

Gary

[copper marlin]

right

like

[ruby wedge]

mhm

[copper marlin]

put these values in that

$D= \sqrt{(-5y)^2 - 4y(6y-1)}$

[modern solstice]

Gary

[copper marlin]

now simplify

[ruby wedge]

root y^2 + 4

[copper marlin]

$D= \sqrt{25y^{2}- 24y^{2}+4y)}$

[modern solstice]

Gary

[copper marlin]

$D= \sqrt{y^{2}+4y}$

[modern solstice]

Gary

[copper marlin]

do u know this property

of sqrt

which is

all the values inside the sqrt

will be

0 or greater

[ruby wedge]

positive

[copper marlin]

then 0

yeh

[ruby wedge]

yes

[copper marlin]

which implies

[ruby wedge]

which means

y^2 + 4y >=0?

then solve fr y

[copper marlin]

$y^{2}+4y>=0$

[modern solstice]

Gary

[copper marlin]

yeh

[ruby wedge]

cool

lemme try solving for y, i'll get back to u in a min

[copper marlin]

u can use wavy curve method or smth

u know that one?

try

[ruby wedge]

y>=0, y<=-4

[ruby wedge]

idk what that is

I'm just starting to learn about domain and range etc

[copper marlin]

u still did it the way i wanted

good

stuff

[copper marlin]

this is correct

[ruby wedge]

so now this in interval notation form would be (-inf, 4) U (0,inf)

?

[copper marlin]

4 and 0 will be included

[ruby wedge]

oh yes

[copper marlin]

.

yeh

[ruby wedge]

so big brackets

[copper marlin]

yep

]

square

brackets

[ruby wedge]

alr

thanks

[copper marlin]

other then that

notation

is correct

[ruby wedge]

understood

for working out range

for functions like this

is this what needs to be done

[copper marlin]

$y \epsilon (-\inf, 4) U (0, \inf)$

its like

[modern solstice]

Gary

[copper marlin]

y belongs

to that

set

[ruby wedge]

oh yes

[copper marlin]

nice way to put it

wrong

emoji

nvm

lmfao

[ruby wedge]

anyways

for functions like these

is this the method to work out range

[copper marlin]

i like when u teach smth to a person and they smart enough to pick it up in the first try

[copper marlin]

i mean when the thing is quadratic

after u took

everything

on one side

yeh

this will do it

sometimes

its much simple

[ruby wedge]

cool

[copper marlin]

let me

show one

example

[ruby wedge]

alr

[copper marlin]

$y = 1/x^2$

[modern solstice]

Gary

[copper marlin]

$x = 1/\sqrt{y}$

[modern solstice]

Gary

[copper marlin]

in this case

there was a

way to take y on one side

and x on another

this is real easy

to deal with

u just take what values

of y u can

fit there

which is?

@ruby wedge

[ruby wedge]

uhh, not sure I'm following you here

y>0 tho

[copper marlin]

yepppp

thats

range

for this one

[ruby wedge]

alr

[copper marlin]

easy

https://tenor.com/view/lucifer-helltaker-cute-dance-moves-gif-17570421

[ruby wedge]

so rlly u just have to make it a fraction, quadratic or something to use a rule such as denominators of fractions can't be equal to 0 or such

[copper marlin]

yep

u just have to find

what values of y is

possible

for range

and when its about domain

its just wat values of

x is possible

@ruby wedge u are an expert now

xd

🗣️ 🔥

[ruby wedge]

hardly lol

[copper marlin]

solve 100 problems

u good

then

[ruby wedge]

can you help me with this

[copper marlin]

yeh

dead

simple

[ruby wedge]

i tried moving everyhting to one side

[copper marlin]

are u suppose to

find

u know

range?

[ruby wedge]

first domain

then range

[copper marlin]

domain is easy

x + 2 > 0

x > -2

simple

[ruby wedge]

wait what

[copper marlin]

i meant

domain

not range

sorry

[copper marlin]

values of x possible

in the numerator u can take any x

but in the denominator

x + 2 > 0

x > -2

so

domain is x > -2

is that

make sense

[ruby wedge]

yes

then range?

[copper marlin]

okay so

$y\sqrt{x+2} = x$

[modern solstice]

Gary

[copper marlin]

well u see

that sqrt

is of

no good

so

what u do is

square both sides

$y^{2}(x+2)= x^2$

[modern solstice]

Gary

[copper marlin]

now its again

quadratic

$0 = x^2 - y^2x - 2y^{2}$

[modern solstice]

Gary

[ruby wedge]

yes I see it now

[copper marlin]

quadratic

so u see u gotta have to sometime

square and stuff too

to get the

shape u can

work with

$\sqrt{y^{4} + 8y^2}$

[modern solstice]

Gary

[copper marlin]

$y^{4} + 8y^2 >= 0$

[modern solstice]

Gary

[copper marlin]

$y^{2}(y^2 + 8) >= 0$

[modern solstice]

Gary

[copper marlin]

wait wtf

[ruby wedge]

I don;t get this one

[copper marlin]

is this making sense

how we got here

[ruby wedge]

yes

[copper marlin]

u get that?

[ruby wedge]

yes

[copper marlin]

now u do

$y^{2}(y^2 + 8) >= 0$

[modern solstice]

Gary

[copper marlin]

u see this is alwayssssssssss true

y^2 is always positive

which means

y is

the whole

R real number

line

[ruby wedge]

which means

y>=0

y=0

but also y<=0?

which means range is all real y in this case

[copper marlin]

yepp

$y\ \epsilon\ R$

[modern solstice]

Gary

[ruby wedge]

how is this true?

[copper marlin]

y is always

y^2

which means

negative

will also

become

positive

$y^{2}(y^2 + 8) >= 0$

[modern solstice]

Gary

[copper marlin]

this stays

always

0 or greater

👍

[ruby wedge]

oh I understand

[copper marlin]

yep

i got them checked

our both

answers

are correct

[ruby wedge]

nice

this has been a lot of help

thanks @copper marlin

[prime phoenix]

@ruby wedge has given 1 rep to @storm linden

[copper marlin]

good to know u got some help :)

https://tenor.com/view/rhythm-heaven-fever-megamix-ds-tambourine-gif-20292579

[ruby wedge]

+close