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. Show also that f (b) is open for any open set B C A.
Answer to relevant Questionsa. Let f: Rn → R be a continuously differentiable function. Show that f is not 1-1. b. Generalize this result to t the case of a continuously differentiable function f: Rn → Rm with m < n.Fauvism-Fauve means wild beasts How do you feel when you look at Dance (fig.32.13). Describe Matisse's style.Surrealism is a movement devoted to expressing in the conscious life, the workings of the unconscious mind. There are no rational controls on words or images.What did the architecture in the late 20th century represent and reflect?Who were the imagists? What were they trying to achieve?
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