a. Ta có:
$f(x)\le2,\forall x\in[-1;3]$
$\Leftrightarrow \left\{\begin{array}{l}f(-1)\le 2\\f(3)\le2\end{array}\right.$
$\Leftrightarrow \left\{\begin{array}{l}-(m-1)+2m-3\le2\\3(m-1)+2m-3\le2\end{array}\right.$
$\Leftrightarrow \left\{\begin{array}{l}m-2\le2\\5m-6\le2\end{array}\right.$
$\Leftrightarrow m\le\dfrac{8}{5}$