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a x^2f(1/x) +f(x) =x/(x+1)

Source: Israel Joseph Gillis Mathematical Olympiad 1995 p8 / Italy 1998 TST p1

February 16, 2020
functional equationfunctionalfunctionalgebra

Problem Statement

A real number α\alpha is given. Find all functions f:R+→R+f : R^+ \to R^+ satisfying αx2f(1x)+f(x)=xx+1\alpha x^2f\left(\frac{1}{x}\right) +f(x) =\frac{x}{x+1} for all x>0x > 0.
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