f(x)=3x+2
g(x)=-2x^2-3x+5
Find g(f(x))
@Jhannybean

- anonymous

f(x)=3x+2
g(x)=-2x^2-3x+5
Find g(f(x))
@Jhannybean

- Stacey Warren - Expert brainly.com

Hey! We 've verified this expert answer for you, click below to unlock the details :)

- katieb

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

- anonymous

so first I would combine them?

- anonymous

so
3x+2-2x^2-3x+5=g(f(x))

- anonymous

g(f(x))=-2x^2+7
right?@Jhannybean

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- jim_thompson5910

g(f(x)) means you start with g(x), then you replace x with f(x) like this
g(x)=-2x^2-3x+5
g(f(x))=-2(f(x))^2-3(f(x))+5 ... replace ALL copies of x with f(x)
g(f(x))=-2(3x+2)^2-3(3x+2)+5 ... on the right side, replace ALL copies of f(x) with 3x+2
now expand and simplify

- anonymous

ok so @jim_thompson5910 was @Jhannybean wrong with how she show'd me the other problems?

- jim_thompson5910

no I didn't say that

- anonymous

i know but this isn't how she showd me

- jim_thompson5910

its possible before you were finding f(x) + g(x) or f(x) - g(x)
but now you've moved onto composite functions

- anonymous

so i wanna make sure i did the others correct
ly

- jim_thompson5910

hopefully you know the difference between them?

- anonymous

they were all composite functions?

- jim_thompson5910

oh they were? are you sure?

- anonymous

yup, thats the entire worksheet

- jim_thompson5910

alright, then yeah, it was gone about the wrong way

- jim_thompson5910

use the method I showed above

- anonymous

uhhh great so would
f(x)=-3+2
g(x)=3x^2-x+2
Find (f+g)(x)
(f+g)(x)=3x^2-4x
is that right?
@jim_thompson5910

- jim_thompson5910

oh those aren't composite functions

- jim_thompson5910

(f+g)(x) = f(x) + g(x)

- jim_thompson5910

that's not a composite function

- anonymous

what's the difference?

- jim_thompson5910

f(g(x)) or g(f(x))
those are composite functions

- anonymous

ooooooooooo

- anonymous

but was it still right?

- jim_thompson5910

the difference is that with composite functions, you were plugging one entire function into the input of another

- jim_thompson5910

f(x)=-3+2 is that right??

- anonymous

yup

- jim_thompson5910

there's no x?

- anonymous

there is it's -3x+2

- anonymous

my bad

- jim_thompson5910

so
f(x) = -3x+2
g(x) = 3x^2-x+2
?

- anonymous

yup

- anonymous

find (f+g)(x)

- anonymous

I got 3x^2-4x

- jim_thompson5910

(f+g)(x) = f(x) + g(x)
(f+g)(x) = -3x+2 + 3x^2-x+2
(f+g)(x) = 3x^2-4x+4

- anonymous

u sure?

- anonymous

I got 3x^2-4x
cuz don't the -2 n +2 cancel eachother out?

- jim_thompson5910

the two '2's are positive though

- jim_thompson5910

f(x) = -3x+2
g(x) = 3x^2-x+2

- anonymous

ooooo ur right

- jim_thompson5910

silly mistake

- jim_thompson5910

but you pretty much got it

- anonymous

haha :)

- anonymous

and this one too?
f(x)=x-1
g(x)=2x^2-2x-5
Find g(f(x))
g(f(x))=2x^2-6x-1
is that right?

- jim_thompson5910

yep, you got it

- anonymous

u rock!!!!!!!!!!!!!!!!!!!!!!!

- jim_thompson5910

thx lol

- anonymous

well that took long

- anonymous

wait so g(f(x))=-2(3x+2)^2-3(3x+2)+5 would simplify to
(-6x+-4)^2-(9x+6)5
@jim_thompson5910

- anonymous

@genius12 it was three problems

- anonymous

ok lol

- jim_thompson5910

not sure how you got (-6x+-4)^2-(9x+6)5

- anonymous

multiply

- jim_thompson5910

btw you do NOT distribute the -2 through to (3x+2)
you have to FOIL out (3x+2)^2 first, then you can distribute

- anonymous

o one sec

- anonymous

(21x+4)

- jim_thompson5910

not sure how you got (3x+2)^2 to turn into 21x+4

- anonymous

-18x^2-33x-9

- anonymous

it's magic, it's magic.

- anonymous

I'm a lil confused

- jim_thompson5910

what do you get when you FOIL out or expand (3x+2)^2
keep in mind that
(3x+2)^2 = (3x+2)(3x+2)
(3x+2)^2 = 3x(3x+2) + 2(3x+2)
(3x+2)^2 = ???

- anonymous

@jim_thompson5910
my final answer to the problem would be -3(2x+3)(3x+1)

- anonymous

is that correct? lol btw I love how there are like 5 ppl just watching my problem

- jim_thompson5910

it's that fascinating lol, but that's if they want you to factor
but I'm assuming they just want you to write it in standard form

- anonymous

yeah, I think ur right, in that case it'd be -18x^2-33x-9 i think

- jim_thompson5910

correct

- anonymous

coolio ty!!!!!!!!!!!!!!!!!!!!

- jim_thompson5910

g(f(x))=-2(3x+2)^2-3(3x+2)+5
g(f(x)) = -18x^2-33x-9

- jim_thompson5910

yw

Looking for something else?

Not the answer you are looking for? Search for more explanations.