Question 94
Let $f: \mathbb{R} \to \mathbb{R}$ be such that for all $x, y \in \mathbb{R}$,
$$
|f(x + y)| = |f(x) + f(y)|.
$$
Prove that $f(x + y) = f(x) + f(y)$ for all $x, y \in \mathbb{R}$.
$$
|f(x + y)| = |f(x) + f(y)|.
$$
Prove that $f(x + y) = f(x) + f(y)$ for all $x, y \in \mathbb{R}$.