TITLE: finding the value of $f(2001) $ if.....
QUESTION [9 upvotes]: if $f (\frac{x}{y}) =\frac{f(x)}{y} $ and $f(2000)=1$ ; then what's the value of $f(2001)$.
I tried hard but can't figured out anything. please help me, how can I proceed?

REPLY [9 votes]: Put $x=y \neq 0$ and we get
$$f(1)={f(x)\over x} \Rightarrow f(x)=f(1)x.$$
Since $f(2000)=1$, $f(1)=1/2000$. Therefore
$$f(2001)={2001\over2000}.$$