Question 25
Let $f : (0, \infty) \to \mathbb{R}$ be such that for all $x, y \in (0, \infty)$,
$$
f(x + y) = f\left(\frac{x + y}{xy}\right) + f(xy).
$$
Show that $f(xy) = f(x) + f(y)$ for all $x, y \in (0, \infty)$.
$$
f(x + y) = f\left(\frac{x + y}{xy}\right) + f(xy).
$$
Show that $f(xy) = f(x) + f(y)$ for all $x, y \in (0, \infty)$.