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All functions so that f(x + f(y + z)) + f(f(x + y) + z) = 2y

Source: Austrian Mathematical Olympiad 2000, Part 2, D2, P3

June 28, 2011
functionalgebra unsolvedalgebra

Problem Statement

Find all functions f:Rā†’Rf : \mathbb R \to \mathbb R such that for all reals x,y,zx, y, z it holds that f(x+f(y+z))+f(f(x+y)+z)=2y.f(x + f(y + z)) + f(f(x + y) + z) = 2y.
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