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Source: Romanian District Olympiad 2023 10.4

March 11, 2023
functional equationalgebraFunctional equation in R

Problem Statement

Determine all functions f:Rā†’Rf:\mathbb{R}\to\mathbb{R} such that any real numbers xx{} and yy{} satisfy f(xf(x)+f(y))=f(f(x2))+y.f(xf(x)+f(y))=f(f(x^2))+y.
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