Suppose that f is differentiable on a closed, bounded interval [a, b]. If f[a, 6] = [a, b] and f' is never zero on [a, b], prove that for every x ∈ [a, b] there exist x1 , x2 ∈ (a, b) such that
F(x) = f'(x1)fʹ(x2)(f-1(x) - f-1(a)) + f(a).