Answer
f(g(x))=x
g(f(x))=x
They are inverses of each other.
Work Step by Step
f(g(x))=4($\frac{x-9}{4}$)+9
f(g(x))=x
g(f(x))=$\frac{(4x+9)-9}{4}$
g(f(x))=x
They are inverses of each other because f(g(x)) and g(f(x)) are both equal to x.