Hello again! I am again lost on another problem. I wasn't sure what to call this, so hopefully it's still somewhat understandable. Thank you very much in advance!

The functions f and g are differentiable. For all x, f(g(x)) = x and g(f(x)) = x. If f(3) = 8 and f'(3) = 9, what are the values of g(8) and g'(8)?

(A) g(8) = 1/3 and g'(8) = -1/9

(B) g(8) = 1/3 and g'(8) = 1/9

(C) g(8) = 3 and g'(8) = -9

(D) g(8) = 3 and g'(8) = -1/9

(E) g(8) = 3 and g'(8) = 1/9