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Functional equation

Source: Irish Mathematical Olympiad 2023 Problem 4

May 16, 2023
functionalgebrafunctional equation

Problem Statement

Find all functions f:R→Rf:\mathbb{R} \rightarrow \mathbb{R} with the property that
f(x)f(y)=(xy−1)2f(x+y−1xy−1)f(x)f(y) = (xy - 1)^2f\left(\frac{x + y - 1}{xy - 1}\right)
for all real numbers x,yx, y with xy≠1xy \neq 1.
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