Question

Sorry I had to repost, I left somethings out.

Can you please check my answers?

For the given functions f and g, find the indicated composition.

5. f(x)=7x+9, g(x)=2x-1
Find (f *g)(x)
I got 14x+2

For the given functions f and g, find the indicated composition.

8. f(x)=-5x+3, g(x)=6x+3
(g * f)(x)
I got -30x+18

Find functions f and g so that h(x)= (f *g)(x)

12. h(x)= 1/(x^2-2)
I got (f)=1/x, g(x)=x^2-2

14. h(x)=(-2x+19)^5
I got f(x)x^5, g(x)=-2x+19

Answer 1

If your f*g(x) means f(g(x)), then for problem #5,

f[g(x)] = 7(2x-1) + 9 = 14 x + 2

For problem #12, there may be more than one combination of f and g that result in
f[g(x)] = 1/(x^2-2). The two functions you listed work fine.