Question

HEELP!
Find each of the following functions.
f(x)=2-3x, g(x)=cosx
fog
gof
fof
gog
and state the domain of the function.

please explain to me step by step, not just the answer

Answer 1

f(g(x)) = 2-3(cos(x))
g(f(x)) = cos(2-3x)
f(f(x)) = 2-3(2-3x) = 2-6+9x = 9x-4

Answer 2

thanks, and how would it be for gog?
do you have any idea of how to state the domain of these functions?

Answer 3

here, i will explain the concept of f(g(x)). the idea is that you substitute g(x) in for every x in f(x). therefore, g(g(x)) means you place g(x) back into wherever there is a x in g(x). so try it and post your work. I'll check it.

The domain is just what x values can you put in and get an answer that is not undefined.
So for f(g(x)) = 9x-4. the domain is whatever x values you can put in and get an answer that is not undefined. Therefore, that would be \[-\infty \le x \le +infinity\]