Question: Let f: R R where f(ab) = af(b) + bf(a), for all a, b R. (a) What is f(l)? (b) What is f(0)?

Let f: R → R where f(ab) = af(b) + bf(a), for all a, b ∈ R. (a) What is f(l)? (b) What is f(0)? (c) If n ∈ Z+, a ∈ R, prove that f(an) = nan~l f (a).

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