Question

Mọi người giúp mk với ak

Answer 1

Bài 1:

ĐKXĐ:

a. \(sinx\ne0\Rightarrow x\ne k\pi\)

b. \(sin2x\ne0\Rightarrow2x\ne k\pi\Rightarrow x\ne\dfrac{k\pi}{2}\)

c. \(cosx\ne0\Rightarrow x\ne\dfrac{\pi}{2}+k\pi\)

d. \(cos\left(x+\dfrac{\pi}{4}\right)\ne0\Rightarrow x+\dfrac{\pi}{4}\ne\dfrac{\pi}{2}+k\pi\Rightarrow x\ne\dfrac{\pi}{4}+k\pi\)

e. \(cos2x\ne0\Rightarrow2x\ne\dfrac{\pi}{2}+k\pi\Rightarrow x\ne\dfrac{\pi}{4}+\dfrac{k\pi}{2}\)

f. \(sin\left(x-\dfrac{\pi}{3}\right)\ne0\Rightarrow x-\dfrac{\pi}{3}\ne k\pi\Rightarrow x\ne\dfrac{\pi}{3}+k\pi\)

g. \(sinx+1\ge0\Rightarrow D=R\)

h. \(cosx-2\ne0\Rightarrow D=R\)

i. \(cosx-1\ne0\Rightarrow cosx\ne1\Rightarrow x\ne k2\pi\)

Answer 2

Bài 2:

a.

\(-1\le cosx\le1\Rightarrow-3\le3cosx\le3\Rightarrow-4\le y\le2\)

\(y_{min}=-4\) khi \(cosx=-1\)

\(y_{max}=2\) khi \(cosx=1\)

b.

\(-1\le sinx\le1\Rightarrow-1\le-sinx\le1\) \(\Rightarrow4\le y\le6\)

\(y_{min}=4\) khi \(sinx=1\)

\(y_{max}=6\) khi \(cosx=1\)

c.

\(0\le\sqrt{cosx}\le1\Rightarrow-3\le y\le-2\)

\(y_{min}=-3\) khi \(cosx=0\)

\(y_{max}=-2\) khi \(cosx=1\)

d.

\(0\le sin^2x\le1\Rightarrow2\le y\le3\)

\(y_{min}=2\) khi \(sinx=0\)

\(y_{max}=3\) khi \(sin^2x=1\Leftrightarrow cosx=0\)