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Source: India IMOTC Practice Test 1 Problem 1

May 31, 2024
functional equationalgebraIMOTC

Problem Statement

Find all functions f:Rā†’Rf:\mathbb R \to \mathbb R such that xf(xf(y)+yf(x))=x2f(y)+yf(x)2, xf(xf(y)+yf(x))= x^2f(y)+yf(x)^2, for all real numbers x,yx,y.
Proposed by B.J. Venkatachala
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