Question 52
Find all functions $f : \mathbb{R}^+ \rightarrow \mathbb{R}^+$ such that for all positive real numbers $x$, $y$
$$
\frac{x + f(y)}{x f(y)} = f\left(\frac{1}{y} + f\left(\frac{1}{x}\right)\right)
$$
$$
\frac{x + f(y)}{x f(y)} = f\left(\frac{1}{y} + f\left(\frac{1}{x}\right)\right)
$$