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Not very attractive functional equation.

Source: Polish MO 2008 Second Round (1st day)

February 22, 2008
functionalgebra proposedalgebra

Problem Statement

Find all functions f:Rā†’R f: \mathbb{R} \rightarrow \mathbb{R} for which the equality f(f(x)\minus{}y)\equal{}f(x)\plus{}f(f(y)\minus{}f(\minus{}x))\plus{}x holds for all real x,yx,y.
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