Difference between revisions of "2024 USAJMO Problems/Problem 5"
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| − | + | __TOC__ | |
| + | |||
| + | == Problem == | ||
| + | Find all functions <math>f:\mathbb{R}\rightarrow\mathbb{R}</math> that satisfy | ||
| + | \[ | ||
| + | f(x^2-y)+2yf(x)=f(f(x))+f(y) | ||
| + | \] | ||
| + | for all <math>x,y\in\mathbb{R}</math>. | ||
| + | |||
| + | == Solution 1 == | ||
| + | |||
| + | |||
| + | ==See Also== | ||
| + | {{USAJMO newbox|year=2024|num-b=4|num-a=6}} | ||
| + | {{MAA Notice}} | ||
Revision as of 12:37, 23 March 2024
Contents
Problem
Find all functions 
that satisfy
\[
f(x^2-y)+2yf(x)=f(f(x))+f(y)
\]
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 | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
