perplexus.info :: Just Math : A positive rational function

A positive rational function (Posted on 2019-11-01)

Let Q' denote the set of all positive rational numbers. If f:Q'→Q' satisfies

f(x²f(y)²)=f(x)²f(y),

evaluate f(2019).

No Solution Yet Submitted by Danish Ahmed Khan

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one solution

| Comment 1 of 3

f(x)=1 is a solution

f(x^2*f(y)^2)=1

and

f(x)^2*f(y)=1^2*1=1

not able to find a proof that this is the only solution

Posted by Daniel on 2019-11-01 10:17:10

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