Suppose that I is a nondegenerate interval, that f : I R is differentiable, and that

Question:

Suppose that I is a nondegenerate interval, that f : I → R is differentiable, and that f'(x) ≠ 0 for all x ∈ I.
a) Prove that f-l exists and is differentiable on f(I).
b) Suppose further that I is a closed, bounded interval and that f' is continuous. Prove that (f-1)' is bounded on f(I).