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Functional equation

Source: Swiss Math Olympiad 2010 - final round, problem 6

March 16, 2010
functionalgebra proposedalgebra

Problem Statement

Find all functions f:R↦R f: \mathbb{R}\mapsto\mathbb{R} such that for all x x, y y ∈R \in\mathbb{R}, f(f(x))\plus{}f(f(y))\equal{}2y\plus{}f(x\minus{}y) holds.
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