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f(xf(y)) + f(f(x) + f(y)) = yf(x) + f(x + f(y))

Source: MEMO 2009, problem 1, single competition

October 1, 2009
functionalgebra proposedalgebra

Problem Statement

Find all functions f:R→R f: \mathbb{R} \to \mathbb{R}, such that f(xf(y)) \plus{} f(f(x) \plus{} f(y)) \equal{} yf(x) \plus{} f(x \plus{} f(y)) holds for all x x, y∈R y \in \mathbb{R}, where R \mathbb{R} denotes the set of real numbers.
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