Question: Suppose that f: X Y is differentiable at x and its derivative is nonsingular. Suppose further that f has an inverse f-1: Y X that

Suppose that f: X †’ Y is differentiable at x and its derivative is nonsingular. Suppose further that f has an inverse f-1: Y †’ X that is continuous (i.e., f is a homeomorphism). Then f-1 is differentiable at x with

Df-11x) = (Df(x)-1

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