If f(g(x)) = x for all x and g(f(x)) = x for all x, than yes, the two are inverses.
The functions f and g are differentiable, and f(g(x))=x for all x. If f(3)=8 and f'(3)=9, what are the values of g(8) and g'(8)?
Does this have to do something with the derivatives of inverse functions? I'm not sure because it's f(g(x)). If it is just the derivative of inverse functions then I know what to do.