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f(x) + f(y) = f(xy f(x + y))

Source: Nordic Mathematical Contest 2003 #4

September 24, 2017

functional equationalgebra

Problem Statement

Let

{R^* = R-\{0\}}

be the set of non-zero real numbers. Find all functions

{f : R^* \rightarrow R^*}

satisfying

{f(x) + f(y) = f(xy f(x + y))}

, for

{x, y \in R^*}

and

{ x + y\ne 0 }