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Câu hỏi: Cho hàm số $f\left( x \right)={{\left( {{x}^{2}}-4 \right)}^{-2}}+{{\log }_{\sqrt{3}}}\left( 2x+1 \right)$
A. $\mathbb{R}\backslash \left\{ \pm 2 \right\}.$
B. $\left( -\dfrac{1}{2};+\infty \right).$
C. $\left( 2;+\infty \right).$
D. $\left( -\dfrac{1}{2};+\infty \right)\backslash \left\{ 2 \right\}.$
A. $\mathbb{R}\backslash \left\{ \pm 2 \right\}.$
B. $\left( -\dfrac{1}{2};+\infty \right).$
C. $\left( 2;+\infty \right).$
D. $\left( -\dfrac{1}{2};+\infty \right)\backslash \left\{ 2 \right\}.$
Điều kiện $\left\{ \begin{aligned}
& {{x}^{2}}-4\ne 0 \\
& 2x+1>0 \\
\end{aligned} \right.\Leftrightarrow \left\{ \begin{aligned}
& x\ne \pm 2 \\
& x>-\dfrac{1}{2} \\
\end{aligned} \right.\Leftrightarrow \left\{ \begin{aligned}
& x\ne 2 \\
& x>-\dfrac{1}{2} \\
\end{aligned} \right..$
Tập xác định: $D=\left( -\dfrac{1}{2};+\infty \right)\backslash \left\{ 2 \right\}.$
& {{x}^{2}}-4\ne 0 \\
& 2x+1>0 \\
\end{aligned} \right.\Leftrightarrow \left\{ \begin{aligned}
& x\ne \pm 2 \\
& x>-\dfrac{1}{2} \\
\end{aligned} \right.\Leftrightarrow \left\{ \begin{aligned}
& x\ne 2 \\
& x>-\dfrac{1}{2} \\
\end{aligned} \right..$
Tập xác định: $D=\left( -\dfrac{1}{2};+\infty \right)\backslash \left\{ 2 \right\}.$
Đáp án D.