# f có là song ánh?

Let $a,b\in \mathbb{R}^*$ and $f: \mathbb{R}\rightarrow \mathbb{R}$ such that $f(x) = ax$ if $\ x\in \mathbb{Q}$  $=bx$ if $x\in\mathbb{R}\backslash \mathbb{Q}$. Prove that $f$ is bijective $\Leftrightarrow \dfrac {a}{b}\in \mathbb{Q}$.