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Functional Equation

Source: Bulgarian IMO TST 2005, Day 1, Problem 3

July 7, 2013
functionalgebra proposedalgebra

Problem Statement

Let R∗\mathbb{R}^{*} be the set of non-zero real numbers. Find all functions f:R∗→R∗f : \mathbb{R}^{*} \to \mathbb{R}^{*} such that f(x2+y)=(f(x))2+f(xy)f(x)f(x^{2}+y) = (f(x))^{2} + \frac{f(xy)}{f(x)}, for all x,y∈R∗x,y \in \mathbb{R}^{*} and −x2≠y-x^{2} \not= y.
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