Question 138
A function $f : \mathbb{Q}_+ \to \mathbb{Q}_+$, where $\mathbb{Q}_+$ denotes the (strictly) positive rational numbers, satisfies
$$
f(f(x) + f(y)) = \frac{xy}{x+y}
$$
for any $x, y \in \mathbb{Q}_+$. Given $f(1) = 2023$, find $f(2023)$.
$$
f(f(x) + f(y)) = \frac{xy}{x+y}
$$
for any $x, y \in \mathbb{Q}_+$. Given $f(1) = 2023$, find $f(2023)$.