Question: Let S = {f: [a, b] R such that f(a+b) = f(a) + 2(b)}. (A) Show that there exists the additive identity of the

Let S = {f: [a, b] R such that f(a+b) = f(a)

Let S = {f: [a, b] R such that f(a+b) = f(a) + 2(b)}. (A) Show that there exists the additive identity of the set, and find it. (solution) (B) Determine whether the set is closed under addition or not. (solution) (C) Determine whether the set is closed under scalar multiplication or not. (solution) (D) Determine whether the set is a vector space or not. (solution)

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