MathDB
f(y(f(x)-x))= f(x)/y - f(y)/x for x,y \ne 0, f(x) \ne x

Source: II Brazilian Olympic Revenge 2003 p6

April 23, 2020
functional equationfunctionalalgebra

Problem Statement

Find all functions f:R∗→Rf:R^{*} \rightarrow R such that f(x)≠xf(x)\not = x and f(y(f(x)−x))=f(x)y−f(y)x f(y(f(x)-x))=\frac{f(x)}{y}-\frac{f(y)}{x} for any x,y≠0x,y \not = 0.
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