Question 4
Find all functions $f$ from the positive reals to the positive reals such that $$
\frac{f(w)^2 + f(x)^2}{f(y^2)+f(z^2)} = \frac{w^2+x^2}{y^2+z^2}
$$ for all positive real numbers $w$, $x$, $y$, $z$ satisfying $wx=yz$.
\frac{f(w)^2 + f(x)^2}{f(y^2)+f(z^2)} = \frac{w^2+x^2}{y^2+z^2}
$$ for all positive real numbers $w$, $x$, $y$, $z$ satisfying $wx=yz$.