6

Part of 2003 Czech-Polish-Slovak Match

Problems(1)

Function: f(f(x) + y) = 2x + f(f(y) − x)

Source: Czech-Polish Slovak 2003 Q6

Find all functions

f : \mathbb{R} \to \mathbb{R}

that satisfy the condition f(f(x) + y) = 2x + f(f(y) - x) \text{ for all } x, y \in\mathbb{R}.

functionalgebra unsolvedalgebra