Sunday, May 28, 2017

Functional equation, find particular value given f(ab)=bf(a)+af(b)

Let f(x) be a function such that f(ab)=bf(a)+af(b) for all nonzero real numbers. Given that f(4)=3, which of the following is a possible value of f(2018)?




(A) 0 (B) 34 (C) 43 (D) 1512 (E) 2688



By substitution, it's easy to find that f(1)=0 and f(2)=34. But how can I get to f(2018)?

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