MathDB
Double functional equation

Source: IMO Shortlist 2000, A3

May 9, 2007
functionalgebrafunctional equationIMO Shortlist

Problem Statement

Find all pairs of functions f:R→R f : \mathbb R \to \mathbb R, g:R→Rg : \mathbb R \to \mathbb R such that f \left( x + g(y) \right) = xf(y) - y f(x) + g(x)  \text{for all } x, y\in\mathbb{R}.
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