Question: Let A C Rn be an open set and f : A Rn a continuously differentiable 1-1 function such that det f1 (x) 0

Let A C Rn be an open set and f : A→ Rn a continuously differentiable 1-1 function such that det f1 (x) ≠ 0 for all . Show that f (A) is an open set and f -1: f (A) →A is differentiable. Demonstrate also that f (b) is open for any open set B C A.

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