1. Consider the sets D = {: ne J}, E = DU {0}. (a) Find a continuous function f : (0, 1)→ R such that its image f((0, 1)) = D. If no such function exists, give reason. (b) Find a continuous function f: E→ R such that its image f(E) = D. If no such function exists, give reason. 2. Find in your notes or text the (counter)example used to refute this statement: If a function is continuous and its inverse exi

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