Tìm tập xác định của các hàm số:
$\begin{array}{l}
1)y = \log _2\sqrt {\frac{x - 3}{x + 1}} \\
2)y = \sqrt {\log_{\frac{1}{2}}\frac{x - 1}{x + 5}}  - {\log _2}\sqrt {x^2 - x - 6} \\
3)y = {\log _3}\frac{x^2 + 4x + 3}{x - 2}
\end{array}$
1) Lập điều kiện:
$\left\{ \begin{array}{l}
X \ne 1\\
\frac{{X - 3}}{{X + 1}} > 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} X\neq 1\\\left[\begin{array}{l} X>3\\X<-1 \end{array} \right.\end{array} \right.$
Từ đó suy ra tập xác định của hàm số là $D = ( - \infty , - 1) \cup (3, + \infty )$
 

2)  Đk:
$\begin{array}{l}\left\{ \begin{array}{l}
{\log _{\frac{1}{2}}}\frac{{X - 1}}{{X + 5}} \ge 0\\
{X^2} - X - 6 > 0\\\frac{X-1}{X+5}>0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
0 < \frac{{X - 1}}{{X + 5}} \le 1\\
X < - 2 \vee X > 3
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l} X>1\vee X<-5\\ \frac{X-1}{X+5}-1\leq 0\\X<-2\vee X>3\end{array} \right.\Leftrightarrow \left\{ \begin{array}{l} X>1\vee X<-5\\\frac{6}{X+5}\geq 0\\X<-2\vee X>3 \end{array} \right.\\ \Leftrightarrow \left\{\begin{array}{l} X>1\\ X>3 \end{array} \right.\end{array}$
Suy ra tập xác định là $D=(3;+\infty)$

3) Đk: $ \frac{{{X^2} + 4X + 3}}{{X - 2}} > 0$
$\Leftrightarrow \left[\begin{array}{l} \left\{ \begin{array}{l} X^2+4X+3>0\\X-2>0 \end{array} \right.\\\left\{ \begin{array}{l} X^2+4X+3<0\\X-2<0 \end{array} \right. \end{array} \right.$
$\Leftrightarrow \left\{ \begin{array}{l} \left[ \begin{array}{l} X>-1\\X<-3 \end{array} \right.\\X>2 \end{array} \right.\vee \left\{ \begin{array}{l}-3<X<-1 \\X>2 \end{array} \right.$

Từ đó rút ra được tập xác định là $ D = ( - 3, - 1) \cup (2, + \infty )$

Thẻ

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