Calculate logs

[round osprey]

<@&286206848099549185>

[round osprey]

<@&286206848099549185>

[round osprey]

<@&286206848099549185>

@silver portal do u mind helping

[sinful cairn]

do a thing

use a^2 - b^2 = a+b)*(a-b)

and write 2 log 5 as log 25

so the ques becomes

3 log 10 * [ 3 log 2/5 ] * [ 2 log 10 ] / log (0.4)

log 0.4 = log 2 / 5

so therefore the sol is 18 * ( log 10 ) ^2

and if you have log with base 10 as defined

then its just 18

[rocky gorge]

hmmm

[round osprey]

thanks for the help and the explanation

[sinful cairn]

your welcome

[round osprey]

also im confused on finding the domain for fog

[sinful cairn]

wait

[sinful cairn]

bro

fog = -1 / x^2

domain are set of input values

so x^2 ≠ 0

so x ≠ 0

so domain = R - {0}

[round osprey]

it says its wrong

[sinful cairn]

try writing x≠0

[sinful cairn]

btw what software is it

free?

[round osprey]

yea thats what i did

[round osprey]

no

[sinful cairn]

...

[sinful cairn]

then not for me lol

[round osprey]

ok

but werent u supposed to find domain of f(x) or g(x) if this doesnt work

[sinful cairn]

i cant understand where we r backing

-∞ < x < 0

0 < x < ∞

try this

[round osprey]

its wrong

[sinful cairn]

i m not doing it anymore

[limpid tree]

wassup gojo

[round osprey]

yo

mind helping me

[limpid tree]

what you need

[round osprey]

need to find domain for fog (x)

[limpid tree]

well f o g (x) domain depends on the domain of g and f

[round osprey]

yea

domain of f is x<-1, 1<x<1, x>1

[limpid tree]

yea

[round osprey]

g is 1<= x<=1

[limpid tree]

so f o g = f(g(x))

[round osprey]

Yep

[limpid tree]

So we are plugging in values between [-1, 1] in g

and get values out between f([0,1])

Now since f must not be 1

[round osprey]

Okay

[limpid tree]

we actually should make [0,1) exclude the 1

and the one is caused by x = 1 and x = -1

so those values of x are not part of the domain

also f o g = f(g(x)) = -1/x² so is there another value that is not allowed?

[round osprey]

i dont think so

what would the domain be

[limpid tree]

0 is also not allowed

so x must not be -1, 0 or 1

[round osprey]

hm it says its wrong

[limpid tree]

we are not finished

what did you even type

g(x) domain was [-1;1]

now with f(g(x)) it should be (-1; 0) U (0;1)

[round osprey]

-1 < x<1, and 0<x<1?

[limpid tree]

this doesnt make sense

it's -1 < x < 1 without 0

[round osprey]

oh

-1 < x< 1

[limpid tree]

or -1 < x < 0 U 0 < x < 1

[round osprey]

is that it

[limpid tree]

no mayne

the 0 is included

dont just type anything

[round osprey]

-1 < x< 0, 0 < x<1

[limpid tree]

yes

[round osprey]

is there any <=?

or

[limpid tree]

do you even listen what i wrote or do you just want straight solutions?

[round osprey]

I did

i thought it was the final answer

[limpid tree]

-1 < x< 0 or 0 < x<1
final

[round osprey]

I entered that

It was incorrect

[limpid tree]

try [-1;1]\{0}

[limpid tree]

The problem is you are trying find the domain just by looking at f(g(x)) but you have to consider the previous domains too meaning composite functions are much more conplicated

[limpid tree]

I made a slight mistake when I explained, the -1 and 1 are part of the domain the 0 is not

[round osprey]

Oh ok thanks

[round osprey]

It still says incorrect

[sinful cairn]

then i m done

i m just a student

[sinful cairn]

thats what i did

R - {0}

[limpid tree]

Can you send a picture?

-1 <= x < 0 or 0 < x <= 1

[limpid tree]

But it cannot be R if g(x) domain is |x| <= 1

[sinful cairn]

doesnt it independent of g(x)

@tall oyster

[limpid tree]

Thats my point it does depend

[sinful cairn]

how

[limpid tree]

"Note that the domain of f composed with g is the set of all x such that x is in the domain of g and
g(x) is in the domain of f(x)"

https://courses.lumenlearning.com/waymakercollegealgebra/chapter/domain-of-a-composition/#:~:text=The domain of a composite function f(g(x),in the domain of f .

[sinful cairn]

ok

so while writing fog

we write f { g(x) }

so with value not in g(x) it will become undefined

thanks

[limpid tree]

Basically find all values of x such that g(x) is in the domain of f(x) with respect to the domain of g(x)

[sinful cairn]

yeah

so we need the common domian btw f(x) and g(x)

[limpid tree]

yeah kinda

[sinful cairn]

thanks man

[limpid tree]

$f o g = f(g(x)) = \frac{1}{g^2(x) - 1}\$

So that would mean basically:

$\ g(x) < 1$ or $g(x) > 1$ but we can leave $g(x) > 1$ out since the range of g(x) is between 0 and 1

That was the idea

[harsh adder]

adonhs

[round osprey]

yea this was correct thanks

[limpid tree]

Well then you typed somethin wrong or they only accept this kind of notation