show that f and g are inverses of each other by verifying that f(g(x))=x =g(f(x))

Question

f(x)=4+x/x, g(x)=4/x-1

Answer 1

You MUST correctly parenthesize each of these functions to get what is intended.  Once you do that, just do the algebra for f(g(x)) and you should get x as the result, thus proving that f & g are inverses of each other.