5

Part of 2001 Czech-Polish-Slovak Match

Problems(1)

Functional: f(x^2+y)+f(f(x)-y)=2f(f(x))+2y^2

Source: Czech-Polish-Slovak 2001 Q5

Find all functions

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

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

functionlimitalgebra unsolvedalgebra