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1992 IMO Problems/Problem 2

Revision as of 19:58, 6 October 2023 by Tomasdiaz (talk | contribs) (Created page with "==Problem== Let <math>\mathbb{R}</math> denote the set of all real numbers. Find all functions <math>f:\mathbb{R} \to \mathbb{R}</math> such that <cmath>f\left( x^{2}+f(y)...")
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Problem

Let $\mathbb{R}$ denote the set of all real numbers. Find all functions $f:\mathbb{R} \to \mathbb{R}$ such that

\[f\left( x^{2}+f(y) \right)= y+(f(x))^{2} \hspace{0.5cm} \forall x,y \in \mathbb{R}\]

Solution

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