Question

Need help!!
In each case, function f and g are defined for xER. For each pair of functions, determine the expression and the domain of f(g(x)) and g(f(x)). Graph each result.
a) f(x)= 3 x^2, g(x)= x-1

Answer 1

This problem requires you to use a method called composition of functions.

So in the case of f(g(x)), you are putting g(x) into f(x). So that everywhere you see an x in f(x), you replace it with the function g(x).
So, f(g(x)) is 3(x-1)^2

Hopefully that gets you started

Answer 2

ok so for the f(g(x)) = x-1
x-1 =3x^2+x-1

Answer 3

so it be like this

Answer 4

@Tuggaro

Answer 5

\[fg(x)=f(g(x))\]\[=f(x-1)\]\[=3(x-1)^2\]

Answer 6

ok

Answer 7

why u write 3

Answer 8

bcoz u say that \[f(x)=3x^2\]

Answer 9

but then where is x square go

Answer 10

oh ok

Answer 11

so know what I have to do

Answer 12

\[gf(x)=g(f(x))\]can u do this?

Answer 13

yeah sure

Answer 14

g(f(x))=3x^2
= 3x^2+x-1

Answer 15

it suppose to be \[gf(x)=g(f(x))\]\[=g(3x^2)\]\[=3x^2-1\]

Answer 16

nope i don't

Answer 17

Please close the question if you no longer need help :)

Answer 18

Still need help!!