Answer
f(g(x))=$\frac{5x+25}{9}$-9
g(f(x))=$\frac{5x-4}{9}$
They are not inverses.
Work Step by Step
f(g(x))=5($\frac{x+5}{9}$)-9
f(g(x))=$\frac{5x+25}{9}$-9
g(f(x))=$\frac{(5x-9)+5}{9}$
g(f(x))=$\frac{5x-4}{9}$
They are inverses of each other because f(g(x)) and g(f(x)) are not equal to x.