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f(x + y) = g (1/x+1/y) (xy)^{2008} , xy\ne 0 , find f,g:R -> R

Source: KJMO 2008 p7

May 2, 2019

algebrafunctional equationfunctions

Problem Statement

Find all pairs of functions

f; g : R \to R

such that for all reals

x.y \ne 0

f(x + y) = g \left(\frac{1}{x}+\frac{1}{y}\right) \cdot (xy)^{2008}