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f(x - f(y)) = f(x + y) + f(y)

Source: AIMO 2008, TST 6, P3

January 4, 2009
functionalgebra unsolvedalgebra

Problem Statement

Determine all functions f:R↦R f: \mathbb{R} \mapsto \mathbb{R} with x,y∈R x,y \in \mathbb{R} such that f(x \minus{} f(y)) \equal{} f(x\plus{}y) \plus{} f(y)
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