Question 181
Consider a function $f : \mathbb{R} \to \mathbb{R}$. For each $a \in \mathbb{Z}$ denote by $f_a : \mathbb{R} \to \mathbb{R}$, the function defined by $f_a(x) = (x - a)f(x)$. Prove that if there are infinitely many values of $a \in \mathbb{Z}$ such that functions $f_a$ are non-decreasing, then $f$ is monotone.