MathNet 2016-part-04 — 184 problems (EN–VI) Question 88

Let $a, b \in \mathbb{R}$ and the function $f_{a,b}: \mathbb{R} \to \mathbb{R}$, $f_{a,b}(x) = a[x] + b\{x\}$. Prove that this function is bijective if and only if $a^2 = b^2 \ne 0$.