Let A ⊆ R^3 be an non-empty, open, bounded set. Consider function f : A → R^2 such that f (x, y, z) = (y, z). Let B be the range or image of f, i.e., B = {f (x, y, z) | (x, y, z) ∈ A}.

(a) Is A never, sometimes, or always convex? Prove the answer.

(b) Is B never, sometimes, or always open? Prove the answer.

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a set A is sometimes convex Proving this you need to consider the definition of convexity A set A in ... View the full answer