Question

Answer 1

1.

a, \(sin3x\in\left[-1;1\right]\)

\(\Rightarrow y=8+2sin3x\in\left[6;10\right]\)

\(\Rightarrow\left\{{}\begin{matrix}y_{min}=6\\y_{max}=10\end{matrix}\right.\)

Answer 2

1.

c, \(sin2x\in\left[-1;1\right]\)

\(\Rightarrow y=\dfrac{10}{6+sin2x}\in\left[\dfrac{10}{7};2\right]\)

\(\Rightarrow\left\{{}\begin{matrix}y_{min}=\dfrac{10}{7}\\y_{max}=2\end{matrix}\right.\)

Answer 3

1.

b, \(cos\left(2x-\dfrac{\pi}{4}\right)\in\left[-1;1\right]\)

\(\Rightarrow y=4-3cos\left(2x-\dfrac{\pi}{4}\right)\in\left[1;7\right]\)

\(\Rightarrow\left\{{}\begin{matrix}y_{min}=1\\y_{max}=7\end{matrix}\right.\)

Answer 4

2.

a, Hàm số xác định khi:

\(cos\left(x-\dfrac{\pi}{3}\right)\ne0\Leftrightarrow x-\dfrac{\pi}{3}\ne\dfrac{\pi}{2}+k\pi\Leftrightarrow x\ne\dfrac{5\pi}{6}+k\pi\)

Answer 5

2.

b, Hàm số xác định khi:

\(sin4x\ne0\Leftrightarrow4x\ne k\pi\Leftrightarrow x\ne\dfrac{k\pi}{4}\)

Answer 6

2.

c, Hàm số xác định khi:

\(2-2cos2x\ne0\Leftrightarrow cos2x\ne1\Leftrightarrow2x\ne k2\pi\Leftrightarrow x\ne k\pi\)

Answer 7

2.

d, Hàm số xác định khi:

\(1+sin\left(2x-\dfrac{\pi}{4}\right)\ne0\Leftrightarrow sin\left(2x-\dfrac{\pi}{4}\right)\ne-1\Leftrightarrow2x-\dfrac{\pi}{4}\ne k\pi\Leftrightarrow x\ne\dfrac{\pi}{8}+\dfrac{k\pi}{2}\)

Answer 8

2.

e, Hàm số xác định khi:

\(\left\{{}\begin{matrix}sin\left(2x-\dfrac{\pi}{3}\right)\ne0\\cos2x\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne\dfrac{\pi}{6}+\dfrac{k\pi}{2}\\x\ne\dfrac{\pi}{4}+\dfrac{k\pi}{2}\end{matrix}\right.\)