Question

Tìm m để hàm số \(y=\dfrac{1}{\sqrt{mx+3}}+log_2\left(3m-5-x\right)\) xác định trên [-1;2)        

Answer 1

\(\left\{{}\begin{matrix}mx+3>0\\3m-5-x>0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}mx>-3\\x< 3m-5\end{matrix}\right.\)

- Với \(m=0\Rightarrow x< -5\) ko thỏa mãn

- Với \(m>0\Rightarrow\left\{{}\begin{matrix}x>-\dfrac{3}{m}\\x< 3m-5\end{matrix}\right.\)

\(\Rightarrow-\dfrac{3}{m}< x< 3m-5\)

\(\Rightarrow\left\{{}\begin{matrix}-1>-\dfrac{3}{m}\\3m-5\ge2\\\end{matrix}\right.\) \(\Rightarrow\dfrac{7}{3}< m< 3\)

- Với \(m< 0\Rightarrow\left\{{}\begin{matrix}x< -\dfrac{3}{m}\\x< 3m-5\end{matrix}\right.\) \(\Rightarrow x< 3m-5\)

\(\Rightarrow3m-5\ge2\Rightarrow m\ge\dfrac{7}{3}\) (ktm)