6

Part of 2010 Switzerland - Final Round

Problems(1)

Functional equation

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

Find all functions

f: \mathbb{R}\mapsto\mathbb{R}

such that for all

x

y

\in\mathbb{R}

, f(f(x))\plus{}f(f(y))\equal{}2y\plus{}f(x\minus{}y) holds.

functionalgebra proposedalgebra