Find all functions so that $f\left(\frac{x}{f(y)}\right) = \frac{x}{f(x\sqrt{y})}$ I have to find all functions so that
$$ f\left(\frac{x}{f(y)}\right) = \frac{x}{f(x\sqrt{y})} $$
I have no idea how to solve this one. Any help would be appreciated!

$f(x)=\sqrt x$ is a solution of your problem
