Question 18
Find all continuous functions $f : \mathbb{R} \to \mathbb{R}$ with the property that for every $a \in \mathbb{R}$ there exists $b \in \mathbb{R}$ such that, for every $x \in \mathbb{R}$,
$$
f(f(x) + a) = f(x) + b.
$$
$$
f(f(x) + a) = f(x) + b.
$$