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Find all R to R functions with f(f(x)^2 + f(y)) = xf(x) + y

Source: Austrian Mathematical Olympiad 2001, Part 2, D2, P1

June 25, 2011
functionalgebra unsolvedalgebra

Problem Statement

Find all functions f:Rā†’Rf :\mathbb R \to \mathbb R such that for all real x,yx, y f(f(x)2+f(y))=xf(x)+y.f(f(x)^2 + f(y)) = xf(x) + y.
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