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−1 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).
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