Calculus Question?

Question

Let f be a twice-differentiable function such that f(2)=5 and F(5)=2. Let g be the function given by g(x)= f(f(x)).

Explain why there must be a value c for 2 f'(c)= -1

Answer 1

It is a consequence of the Mean Value Theorem.

(The function g(x) is irrelevant to this. Part of another problem?)