Difference between revisions of "2024 USAJMO Problems/Problem 5"
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== Problem == | == Problem == | ||
Find all functions <math>f:\mathbb{R}\rightarrow\mathbb{R}</math> that satisfy | Find all functions <math>f:\mathbb{R}\rightarrow\mathbb{R}</math> that satisfy | ||
| − | + | <cmath>f(x^2-y)+2yf(x)=f(f(x))+f(y)</cmath> | |
| − | f(x^2-y)+2yf(x)=f(f(x))+f(y) | ||
| − | |||
for all <math>x,y\in\mathbb{R}</math>. | for all <math>x,y\in\mathbb{R}</math>. | ||
== Solution 1 == | == Solution 1 == | ||
| − | |||
==See Also== | ==See Also== | ||
{{USAJMO newbox|year=2024|num-b=4|num-a=6}} | {{USAJMO newbox|year=2024|num-b=4|num-a=6}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Latest revision as of 21:42, 9 April 2024
Contents
Problem
Find all functions 
that satisfy
![\[f(x^2-y)+2yf(x)=f(f(x))+f(y)\]](http://latex.artofproblemsolving.com/4/b/d/4bdeaa49c29c972b00378da74fa56558da3d543e.png)
for all 
.
Solution 1
See Also
| 2024 USAJMO (Problems • Resources) | ||
| Preceded by Problem 4 |
Followed by Problem 6 | |
| 1 • 2 • 3 • 4 • 5 • 6 | ||
| All USAJMO Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
