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Difference between revisions of "1990 IMO Problems/Problem 4"

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4. Let <math>\mathbb{Q^+}</math> be the set of positive rational numbers. Construct a function <math>f :\mathbb{Q^+}\rightarrow\mathbb{Q^+}</math> such that <math>f(xf(y)) = \frac{f(x)}{y}</math> for all <math>x, y\in{Q^+}</math>.
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==Problem==
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Let <math>\mathbb{Q^+}</math> be the set of positive rational numbers. Construct a function <math>f :\mathbb{Q^+}\rightarrow\mathbb{Q^+}</math> such that <math>f(xf(y)) = \frac{f(x)}{y}</math> for all <math>x, y\in{Q^+}</math>.
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==Solution==
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{{solution}}
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== See Also == {{IMO box|year=1990|num-b=3|num-a=5}}
  
 
[[Category:Olympiad Algebra Problems]]
 
[[Category:Olympiad Algebra Problems]]
 
[[Category:Functional Equation Problems]]
 
[[Category:Functional Equation Problems]]

Revision as of 13:46, 30 January 2021

Problem

Let $\mathbb{Q^+}$ be the set of positive rational numbers. Construct a function $f :\mathbb{Q^+}\rightarrow\mathbb{Q^+}$ such that $f(xf(y)) = \frac{f(x)}{y}$ for all $x, y\in{Q^+}$.

Solution

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See Also

1990 IMO (Problems) • Resources
Preceded by
Problem 3 		1 • 2 • 3 • 4 • 5 • 6 Followed by
Problem 5
All IMO Problems and Solutions
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