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The function $f(x)$ takes positive real numbers to real numbers, such that \[xf(y) - yf(x) = f \left( \frac{x}{y} \right)\]for all positive real numbers $x$ and $y.$ Find all possible values of $f(100).$ Enter all possible values, separated by commas.

 May 2, 2021
 #1
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The possible values of f(100) are -1, 0, 1.

 May 2, 2021

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