Let
![{\mathbb Q}^ +](/media/m/f/f/e/ffe3629eb28d1ca03bef205d426c4a73.png)
be the set of positive rational numbers. Construct a function
![f : {\mathbb Q}^ + \rightarrow {\mathbb Q}^ +](/media/m/1/1/9/11957f559d8868f9646bcc32eb19803e.png)
such that
for all
![x](/media/m/f/1/8/f185adeed9bd346bc960bca0147d7aae.png)
,
![y](/media/m/c/c/0/cc082a07a517ebbe9b72fd580832a939.png)
in
![{\mathbb Q}^ +](/media/m/f/f/e/ffe3629eb28d1ca03bef205d426c4a73.png)
.
%V0
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 ${\mathbb Q}^ +$.