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Functional equation: f(x(f(y))=f(xy)+x

Source: Czech and Slovak MO, 2002, P6

September 15, 2012
functionalgebra unsolvedalgebra

Problem Statement

Let R+\mathbb{R}^{+} denote the set of positive real numbers. Find all functions f:R+→R+f : \mathbb{R}^{+} \to \mathbb{R}^{+} satisfying for all x,y∈R+x, y \in \mathbb{R}^{+} the equality f(xf(y))=f(xy)+xf(xf(y))=f(xy)+x
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