Question 155
Find all functions $f: \mathbb{R} \to \mathbb{R}$ such that
$$
f(\max\{x, y\} + \min\{f(x), f(y)\}) = x + y \quad (1)
$$
for all $x, y \in \mathbb{R}$.
$$
f(\max\{x, y\} + \min\{f(x), f(y)\}) = x + y \quad (1)
$$
for all $x, y \in \mathbb{R}$.