Đáp án:
$1)D=\mathbb{R}\\2)D=\mathbb{R} \setminus \left\{ \dfrac{\pi}{2}+ k \pi ;k \in \mathbb{Z}\right\}\\ 3)D=\mathbb{R} \setminus \left\{ 1\right\}\\ 4)D=\mathbb{R}\\ 5)D=\mathbb{R} \setminus \left\{ k 2 \pi ;k \in \mathbb{Z}\right\}\\ 6)D=\mathbb{R} \setminus \left\{\dfrac{\pi}{4} + \dfrac{k \pi}{2};k \in \mathbb{Z}\right\}$
Giải thích các bước giải:
$1)\\ y=\sin\dfrac{3x}{2}$
Xác định với mọi $x$
$\text{TXĐ: }D=\mathbb{R}$
$2)\\ y=\dfrac{1}{2\cos x}\\ \text{ĐKXĐ: }\cos x \ne 0\\ \Leftrightarrow x \ne \dfrac{\pi}{2}+ k \pi (k \in \mathbb{Z})\\ \text{TXĐ: }D=\mathbb{R} \setminus \left\{ \dfrac{\pi}{2}+ k \pi ;k \in \mathbb{Z}\right\}\\ 3)\\ y=\cos\dfrac{2x}{x-1}\\ \text{ĐKXĐ: }x-1 \ne 0 \Leftrightarrow x \ne 1\\ \text{TXĐ: }D=\mathbb{R} \setminus \left\{ 1\right\}\\ 4)\\ \sqrt{3-\sin x}\\ \text{Do }\sin x \in [-1;1]\\ \Rightarrow 3-\sin x \in [2;4]$
$\Rightarrow \sqrt{3-\sin x}$ xác định với mọi $x$
$\text{TXĐ: }D=\mathbb{R}\\ 5)\\ y=\dfrac{1}{\cos x-1}\\ \text{ĐKXĐ: }\cos x-1 \ne 0\Leftrightarrow x \ne 1\Leftrightarrow x \ne k 2 \pi (k \in \mathbb{Z})\\ \text{TXĐ: }D=\mathbb{R} \setminus \left\{ k 2 \pi ;k \in \mathbb{Z}\right\}\\ 6)\\ \tan 2x\\ \text{ĐKXĐ: } 2x \ne \dfrac{\pi}{2} + k \pi(k \in \mathbb{Z})\\ \Leftrightarrow x \ne \dfrac{\pi}{4} + \dfrac{k \pi}{2}(k \in \mathbb{Z})\\ \text{TXĐ: }D=\mathbb{R} \setminus \left\{\dfrac{\pi}{4} + \dfrac{k \pi}{2};k \in \mathbb{Z}\right\}$
