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

Source: Czech-Polish-Slovak 2001 Q5

April 30, 2013
functionlimitalgebra unsolvedalgebra

Problem Statement

Find all functions f:Rā†’Rf : \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}.
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