a) Để hàm số đồng biến
thì \(\Rightarrow m^2+m-2>0\)
\(\Rightarrow m^2+2m-m-2>0\\ \Rightarrow m\left(m+2\right)-\left(m+2\right)>0\\ \Rightarrow\left(m-1\right)\left(m+2\right)>0\\ \Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}m-1>0\\m+2>0\end{matrix}\right.\\\left\{{}\begin{matrix}m-1< 0\\m+2< 0\end{matrix}\right.\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}m-1>0\\m+2< 0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}m>1\\m< -2\end{matrix}\right.\)
b) Để hàm số nghịch biến
thì \(\Rightarrow m^2+m-2< 0\)
\(\Rightarrow\left(m-1\right)\left(m+2\right)< 0\\ \Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}m-1< 0\\m+2>0\end{matrix}\right.\\\left\{{}\begin{matrix}m-1>0\\m+2< 0\end{matrix}\right.\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}m-1< 0\\m+2>0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}m< 1\\m>-2\end{matrix}\right.\\ \Rightarrow-2< m< 1\)
