Question 8
Find all functions $f: (0, \infty) \to (0, \infty)$ such that
$$
f\left(f(x) + \frac{y+1}{f(y)}\right) = \frac{1}{f(y)} + x + 1
$$
for all $x, y \gt 0$.
(Dominik Burek)
$$
f\left(f(x) + \frac{y+1}{f(y)}\right) = \frac{1}{f(y)} + x + 1
$$
for all $x, y \gt 0$.
(Dominik Burek)