Question 152
Find all functions $f: \mathbb{R} \to \mathbb{R}$ such that
$$
f(x + f(x)) = f(-x)
$$
for all real numbers $x$ and $f(x) \le f(y)$ for all real numbers $x \le y$.
$$
f(x + f(x)) = f(-x)
$$
for all real numbers $x$ and $f(x) \le f(y)$ for all real numbers $x \le y$.