8

Part of 2003 Kazakhstan National Olympiad

Problems(1)

Function Equation German TST 2003 - f(f(x)+y)=2x+f(f(y)-x)

Source: German TST 2003

Determine all functions

f: \mathbb R \to \mathbb R

with the property f(f(x)+y)=2x+f(f(y)-x), \forall x,y \in \mathbb R.

functionalgebra unsolvedalgebra