Let f be a function, and suppose that A is a subset of the domain of f. The image of A under f is ƒ(A) = {ƒ(x) | x € A}. (a) Consider the function f : R → R given by f(x) = x². Let A = [0, 2] and B = [1,4]. Find ƒ(A) and ƒ(B). Does ƒ(A^B) = ƒ(A)^ƒ(B)? Does f(AUB) = f(A) U ƒ(B)? (b) Find sets A and B so that ƒ(A^B) ‡ƒ(A)Ñ ƒ(B). (c) Let g: R→ R be a function, and let A, B C R. Prove that g(AnB) ≤ g(A)ng(B).

Q: Let f : R → R be a function with the following property: |f (a) – f(b)| < 4|a – b| for all a, b E R.

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A: See the answer below

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