Question

Given the functions:
f(x)=2x+2 g(x)=3/x^2+2 h(x)=sqrt(x-2)

Find the following
1) (f∘g)(-5)
2) (h∘g)(3)
3) (g∘h)(-2)
4) (g∘g)(-2)
5) (f∘h)(12)

Find the following and state the domain:
6) h∘g
7) f∘g
8) g∘f
9) g∘g
10)g∘h

Answer 1

I can't edit but f(x) is suppose to be f(x)=3x+2 I put 2x by mistake!

Answer 2

I'll do one. Do the others in like wise. If you get stuck, come on back with what you did.

(g∘h) = 3/(h^2+2) = 3/(x-2+2) = 3/x
(g∘h)(-2) = 3/-2 = -3/2

The domain of h is x>=2
The domain of g is all reals, since x^2+2 is never zero.
So, the domain of (g∘h) is all reals x >= 2 because you can't have (g∘h)(x) unless h is defined.