Question

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

Answer 1

so first I would combine them?

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

no I didn't say that

Answer 7

i know but this isn't how she showd me

Answer 8

its possible before you were finding f(x) + g(x) or f(x) - g(x)

but now you've moved onto composite functions

Answer 9

so i wanna make sure i did the others correct
ly

Answer 10

hopefully you know the difference between them?

Answer 11

they were all composite functions?

Answer 12

oh they were? are you sure?

Answer 13

yup, thats the entire worksheet

Answer 14

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

Answer 15

use the method I showed above

Answer 16

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

Answer 17

oh those aren't composite functions

Answer 18

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

Answer 19

that's not a composite function

Answer 20

what's the difference?

Answer 21

f(g(x)) or g(f(x))

those are composite functions

Answer 22

ooooooooooo

Answer 23

but was it still right?

Answer 24

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

Answer 25

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

Answer 26

yup

Answer 27

there's no x?

Answer 28

there is it's -3x+2

Answer 29

my bad

Answer 30

so

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

?

Answer 31

yup

Answer 32

find (f+g)(x)

Answer 33

I got 3x^2-4x

Answer 34

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

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

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

Answer 35

u sure?

Answer 36

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

Answer 37

the two '2's are positive though

Answer 38

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

Answer 39

ooooo ur right

Answer 40

silly mistake

Answer 41

but you pretty much got it

Answer 42

haha :)

Answer 43

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?

Answer 44

yep, you got it

Answer 45

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

Answer 46

thx lol

Answer 47

well that took long

Answer 48

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

Answer 49

@genius12 it was three problems

Answer 50

ok lol

Answer 51

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

Answer 52

multiply

Answer 53

btw you do NOT distribute the -2 through to (3x+2)

you have to FOIL out (3x+2)^2 first, then you can distribute

Answer 54

o one sec

Answer 55

(21x+4)

Answer 56

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

Answer 57

-18x^2-33x-9

Answer 58

it's magic, it's magic.

Answer 59

I'm a lil confused

Answer 60

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 = ???

Answer 61

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

Answer 62

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

Answer 63

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

Answer 64

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

Answer 65

correct

Answer 66

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

Answer 67

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

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

Answer 68

yw