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

(Created page with "==Problem== Let <math>\mathbb{R}^+</math> denote the set of positive real numbers. Find all functions <math>f : \mathbb{R}^+ \to \mathbb{R}^+</math> such that for each <math>x...")
 
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==Solution==
 
==Solution==
 
https://www.youtube.com/watch?v=nYD-qIOdi_c [Video contains solutions to all day 1 problems]
 
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]

Revision as of 07:59, 28 August 2022

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]

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