Hàm số xác định \(\Leftrightarrow\left(m-2\right)x^2-2\left(m-3\right)x+m-1\ge0\)
Đặt \(f\left(x\right)=\left(m-2\right)x^2-2\left(m-3\right)x+m-1\ge0\)
\(f\left(x\right)\ge0,\forall x\in R\Leftrightarrow\left\{{}\begin{matrix}a>0\\\Delta\le0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}m-2>0\\\left[-2\left(m-3\right)\right]^2-4\left(m-2\right)\left(m-1\right)\le0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}m>2\\4\left(m^2-6m+9\right)-4\left(m^2-3m+2\right)\le0\end{matrix}\right.\)
\(\Leftrightarrow4m^2-24m+36-4m^2+12m-8\le0\)
\(\Leftrightarrow-12m+28\le0\)
\(\Leftrightarrow m\le\dfrac{7}{3}\)
\(KL:m\in(2;\dfrac{7}{3}]\)
