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Difference between revisions of "2022 IMO Problems/Problem 2"

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https://youtu.be/b5OZ62vkF9Y  [Video Solution by little fermat]
 
https://youtu.be/b5OZ62vkF9Y  [Video Solution by little fermat]
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==See Also==
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{{IMO box|year=2022|num-b=1|num-a=3}}

Revision as of 00:54, 19 November 2023

Problem

Let $\mathbb{R}^+$ denote the set of positive real numbers. Find all functions $f : \mathbb{R}^+ \to \mathbb{R}^+$ such that for each $x \in \mathbb{R}^+$, there is exactly one $y \in \mathbb{R}^+$ satisfying

\[xf (y) + yf (x) \le 2\].

Solution

https://www.youtube.com/watch?v=nYD-qIOdi_c [Video contains solutions to all day 1 problems]

https://youtu.be/b5OZ62vkF9Y [Video Solution by little fermat]

See Also

2022 IMO (Problems) • Resources
Preceded by
Problem 1 		1 • 2 • 3 • 4 • 5 • 6 Followed by
Problem 3
All IMO Problems and Solutions
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