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Functional Equation

Source: India TST 2016 Day 4 Problem 2

July 22, 2016
functional equationfunctionalgebra

Problem Statement

Find all functions f:RRf:\mathbb{R}\to\mathbb{R} such that f(x3+f(y))=x2f(x)+y,f\left(x^3+f(y)\right)=x^2f(x)+y,for all x,yR.x,y\in\mathbb{R}. (Here R\mathbb{R} denotes the set of all real numbers.)