Difference between revisions of "1992 IMO Problems/Problem 2"

(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)...")
 
(Solution)
Line 7: Line 7:
 
==Solution==
 
==Solution==
 
{{solution}}
 
{{solution}}
 +
 +
==See Also==
 +
 +
{{IMO box|year=1992|num-b=1|num-a=3}}
 +
[[Category:Olympiad Geometry Problems]]
 +
[[Category:3D Geometry Problems]]

Revision as of 23:41, 16 November 2023

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.

See Also

1992 IMO (Problems) • Resources
Preceded by
Problem 1
1 2 3 4 5 6 Followed by
Problem 3
All IMO Problems and Solutions