How would you solve this composite function?

Question

Find both f(g(x)) and g(f(x)), given that f(x)=1/2x-2 and g(x)=2x+4.

Answer 1

f(g(x)) you plug g into f and simplify

1/2(2x+4)-2 distribute

x+2-2 subtract

f(g(x))=x

g(f(x)) you plug f into g and simplify

2(1/2x-2)+4 distribute

x-4+4 add

g(f(x))=x

Since they both equal x, these functions are inverses