Đáp án:
\(\begin{array}{l}
1,\\
D = \left[ {0; + \infty } \right)\\
2,\\
D = R\backslash \left\{ 0 \right\}\\
5,\\
D = R\backslash \left\{ {k\pi |k \in Z} \right\}\\
6,\\
D = R\backslash \left\{ {k\pi |k \in Z} \right\}\\
7,\\
D = R\backslash \left\{ {\dfrac{\pi }{8} + \dfrac{{k\pi }}{2}|k \in Z} \right\}\\
8,\\
D = R\backslash \left\{ {\dfrac{{3\pi }}{{20}} + \dfrac{{k\pi }}{2}|k \in Z} \right\}\\
10,\\
D = R\backslash \left\{ 1 \right\}\\
11,\\
D = R\backslash \left\{ { - 1;1} \right\}\\
12,\\
D = R\backslash \left\{ {\dfrac{{5\pi }}{{12}} + \dfrac{{k\pi }}{2}|k \in Z} \right\}\\
14,\\
D = R\backslash \left\{ {\dfrac{{k\pi }}{2}|k \in Z} \right\}
\end{array}\)
Giải thích các bước giải:
Các hàm số đã cho xác định khi và chỉ khi:
\(\begin{array}{l}
1,\\
x \ge 0\\
\Rightarrow TXD:\,\,\,D = \left[ {0; + \infty } \right)\\
2,\\
x \ne 0\\
\Rightarrow TXD:\,\,\,D = R\backslash \left\{ 0 \right\}\\
5,\\
\sin x \ne 0 \Leftrightarrow x \ne k\pi \,\,\,\,\left( {k \in Z} \right)\\
\Rightarrow TXD:\,\,\,D = R\backslash \left\{ {k\pi |k \in Z} \right\}\\
6,\\
\left\{ \begin{array}{l}
\sin x \ne 0\\
\cos x - 1 \ne 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
\sin x \ne 0\\
\cos x \ne 1
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x \ne k\pi \\
x \ne k2\pi
\end{array} \right. \Leftrightarrow x \ne k\pi \,\,\,\left( {k \in Z} \right)\\
\Rightarrow TXD:\,\,\,D = R\backslash \left\{ {k\pi |k \in Z} \right\}\\
7,\\
\sin \left( {2x - \dfrac{\pi }{4}} \right) \ne 0 \Leftrightarrow 2x - \dfrac{\pi }{4} \ne k\pi \\
\Leftrightarrow 2x \ne \dfrac{\pi }{4} + k\pi \Leftrightarrow x \ne \dfrac{\pi }{8} + \dfrac{{k\pi }}{2}\,\,\,\,\,\left( {k \in Z} \right)\\
\Rightarrow TXD:\,\,\,\,D = R\backslash \left\{ {\dfrac{\pi }{8} + \dfrac{{k\pi }}{2}|k \in Z} \right\}\\
8,\\
\cos \left( {2x + \dfrac{\pi }{5}} \right) \ne 0 \Leftrightarrow 2x + \dfrac{\pi }{5} \ne \dfrac{\pi }{2} + k\pi \\
\Leftrightarrow 2x \ne \dfrac{{3\pi }}{{10}} + k\pi \Leftrightarrow x \ne \dfrac{{3\pi }}{{20}} + \dfrac{{k\pi }}{2}\,\,\,\,\left( {k \in Z} \right)\\
\Rightarrow TXD:\,\,\,\,D = R\backslash \left\{ {\dfrac{{3\pi }}{{20}} + \dfrac{{k\pi }}{2}|k \in Z} \right\}\\
10,\\
x - 1 \ne 0 \Leftrightarrow x \ne 1\\
\Rightarrow TXD:\,\,\,D = R\backslash \left\{ 1 \right\}\\
11,\\
{x^2} - 1 \ne 0 \Leftrightarrow \left( {x - 1} \right)\left( {x + 1} \right) \ne 0 \Leftrightarrow \left\{ \begin{array}{l}
x - 1 \ne 0\\
x + 1 \ne 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x \ne 1\\
x \ne - 1
\end{array} \right.\\
\Rightarrow TXD:\,\,\,D = R\backslash \left\{ { - 1;1} \right\}\\
12,\\
\cos \left( {2x - \dfrac{\pi }{3}} \right) \ne 0 \Leftrightarrow 2x - \dfrac{\pi }{3} \ne \dfrac{\pi }{2} + k\pi \\
\Leftrightarrow 2x \ne \dfrac{{5\pi }}{6} + k\pi \Leftrightarrow x \ne \dfrac{{5\pi }}{{12}} + \dfrac{{k\pi }}{2}\,\,\,\,\left( {k \in Z} \right)\\
\Rightarrow TXD:\,\,\,\,D = R\backslash \left\{ {\dfrac{{5\pi }}{{12}} + \dfrac{{k\pi }}{2}|k \in Z} \right\}\\
14,\\
\left\{ \begin{array}{l}
\cos x \ne 0\\
\sin x \ne 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x \ne \dfrac{\pi }{2} + k\pi \\
x \ne k\pi
\end{array} \right. \Leftrightarrow x \ne \dfrac{{k\pi }}{2}\\
\Rightarrow TXD:\,\,\,D = R\backslash \left\{ {\dfrac{{k\pi }}{2}|k \in Z} \right\}
\end{array}\)
