Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

1992 IMO Problems/Problem 2

Revision as of 20:58, 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)...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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

This problem needs a solution. If you have a solution for it, please help us out by adding it.

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1992_IMO_Problems/Problem_2&oldid=199279"