Which statement verifies that $f(x)$ and $g(x)$ are inverses of each other?

A$f(g(x))=x$

B$f(g(x))=x$ and $g(f(x))=-x$

C$f(g(x))=\frac{1}{g(f(x))}$

D$f(g(x))=x$ and $g(f(x))=x$