Question

Tìm m để hàm số y =\(\frac{\sqrt{x-2m+3}}{x-m}+\frac{3x-1}{\sqrt{-x+m+5}}\) xác định trên khoảng (0;1)

Answer 1

ĐKXĐ: \(\left\{{}\begin{matrix}x-2m+3\ge0\\-x+m+5>0\\x\ne m\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge2m-3\\x< m+5\\x\ne m\end{matrix}\right.\)

Để hàm xác định trên khoảng đã cho:

\(\Leftrightarrow\left\{{}\begin{matrix}2m-3\le0\\m+1\ge1\\\left[{}\begin{matrix}m\le0\\m\ge1\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}m\le\frac{3}{2}\\m\ge0\\\left[{}\begin{matrix}m\le0\\m\ge1\end{matrix}\right.\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}m=0\\1\le m\le\frac{3}{2}\end{matrix}\right.\)