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Functional equation: ( 1 + y f(x) )( 1 - y f(x+y) ) = 1

Source: Czech-Polish-Slovak Match, 2009

August 21, 2011
functionsymmetryalgebra 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}^+ that satisfy (1+yf(x))(1−yf(x+y))=1 \Big(1+yf(x)\Big)\Big(1-yf(x+y)\Big)=1 for all x,y∈R+x,y\in\mathbb{R}^+.
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