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Easy, classical FE

Source: Latvian TST for Baltic Way 2019 Problem 2

May 29, 2020
functionfunctional equationalgebra

Problem Statement

Let R\mathbb R be set of real numbers. Determine all functions f:R→Rf:\mathbb R\to \mathbb R such that f(y2−f(x))=yf(x)2+f(x2y+y)f(y^2 - f(x)) = yf(x)^2+f(x^2y+y) holds for all real numbers x;yx; y
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