Find all functions
![f: (0, \infty) \mapsto (0, \infty)](/media/m/7/c/3/7c396c9236f5a09d9743959d7eeccecf.png)
(so
![f](/media/m/9/9/8/99891073047c7d6941fc8c6a39a75cf2.png)
is a function from the positive real numbers) such that
for all positive real numbes
![w,x,y,z,](/media/m/c/5/b/c5b48b088cbbc554d128f84e9ef157d1.png)
satisfying
Author: Hojoo Lee, South Korea
%V0
Find all functions $f: (0, \infty) \mapsto (0, \infty)$ (so $f$ is a function from the positive real numbers) such that
$$\frac {\left( f(w) \right)^2 + \left( f(x) \right)^2}{f(y^2) + f(z^2) } = \frac {w^2 + x^2}{y^2 + z^2}$$
for all positive real numbes $w,x,y,z,$ satisfying $wx = yz.$
Author: Hojoo Lee, South Korea