Đáp án:
Giải thích các bước giải:
a) `ĐK: sin (7x-\frac{\pi}{6}) \ne 0`
`⇔ 7x-\frac{\pi}{6} \ne k\pi\ (k \in \mathbb{Z})`
`⇔ x \ne \frac{\pi}{42}+\frac{k\pi}{7}\ (k \in \mathbb{Z})`
`D=\mathbb{R} \\ {\frac{\pi}{42}+\frac{k\pi}{7}\ (k \in \mathbb{Z})}`
b) `sin^4x+cos^4x`
`=1-2sin^2 x. cos^2 x`
`=1-\frac{1}{2}.sin^2 2x`
`0 \le sin^2 2x \le 1 ⇔ 0 \le \frac{1}{2}.sin^2 2x \le \frac{1}{2}`
`⇔ 1 \ge 1-\frac{1}{2}.sin^2 2x \ge \frac{1}{2}`
`⇔ 1 \ge y \ge \frac{1}{2}`
Min` f(x)=\frac{1}{2}⇔sin^2 2x=1⇔ x=±\frac{\pi}{4}+\frac{k\pi}{2}\ (k \in \mathbb{Z})`
`Max\ f(x)=1⇔x=k\pi\ (k\in \mathbb{Z})`
