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

Source: International competition SRMC 2006 P-1

September 8, 2010
functionalgebra solvedalgebra

Problem Statement

Found all functions f:R→Rf: \mathbb{R} \to \mathbb{R}, such that for any x,y∈Rx,y \in \mathbb{R}, f(x2+xy+f(y))=f2(x)+xf(y)+y.f(x^2+xy+f(y))=f^2(x)+xf(y)+y.
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