ĐKXĐ:

a. \(\left\{{}\begin{matrix}x-1\ge0\\x-3\ne0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x\ge1\\x\ne3\end{matrix}\right.\)  \(\Rightarrow D=[1;+\infty)\backslash\left\{3\right\}\)

b. \(D=R\)

c. \(x+3>0\Rightarrow x>-3\Rightarrow D=\left(-3;+\infty\right)\)

d. \(\left|x-2\right|\ge0\Rightarrow x\in R\Rightarrow D=R\)

TXĐ: D=R\{3;-3}

`@` H/s xác định `<=>{(x+2 >= 0),(2-x >= 0):}<=>{(x >= -2),(x <= 2):}<=>-2 <= x <= 2`

   `=>TXĐ: D=[-2;2]`

`@-2 <= x <= 2`

`<=>{(0 <= x+2 <= 4),(2 >= -x >= -2):}`

`<=>{(0 <= x+2 <= 4),(4 >= 2-x >= 0):}`

`<=>{(0 <= \sqrt{x+2} <= 2),(2 >= \sqrt{2-x} >= 0):}`

   `=>TGT` là `[0;2]`

\(y=\sqrt{x+2}+\sqrt{2-x}\)

y có nghĩa \(\Leftrightarrow\left\{{}\begin{matrix}x+2>0\\2-x>0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x>-2\\x>2\end{matrix}\right.\)

TXD D = \(\left(2;+\infty\right)\)

\(đk\left\{{}\begin{matrix}x+2\ge0\\2-x\ge0\end{matrix}\right.=>\left\{{}\begin{matrix}x\ge-2\\x\le2\end{matrix}\right.\)

\(=>TXĐ:\left[-2;2\right]\)

a, ĐK: \(x\ne\dfrac{k\pi}{2}\)

\(y=f\left(x\right)=\dfrac{1}{tanx}\)

\(f\left(-x\right)=\dfrac{1}{tan\left(-x\right)}=-\dfrac{1}{tanx}=-f\left(x\right)\Rightarrow\) Là hàm số lẻ.

c, \(y=f\left(x\right)=sin^2x+2cosx-3\)

\(f\left(-x\right)=sin^2\left(-x\right)+2cos\left(-x\right)-3\)

\(=\left(-sinx\right)^2+2cosx-3\)

\(=sin^2x+2cosx-3=f\left(x\right)\)

\(\Rightarrow\) Là hàm số chẵn.

b, Xem lại đề.

ĐKXĐ:

a. \(cos\left(x-\dfrac{2\pi}{3}\right)\ne0\Rightarrow x-\dfrac{2\pi}{3}\ne\dfrac{\pi}{2}+k\pi\Rightarrow x\ne\dfrac{\pi}{6}+k\pi\)

b. \(sin\left(x+\dfrac{\pi}{6}\right)\ne0\Rightarrow x+\dfrac{\pi}{6}\ne k\pi\Rightarrow x\ne-\dfrac{\pi}{6}+k\pi\)

c. \(\dfrac{1+x}{2-x}\ge0\Rightarrow-1\le x< 2\)

1.

Hàm số xác định khi \(\left\{{}\begin{matrix}\dfrac{1+x}{1-x}\ge0\\1-x\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-1\le x< 1\\x\ne1\end{matrix}\right.\Leftrightarrow-1\le x< 1\)

2.

Hàm số xác định khi \(cosx+1\ne0\Leftrightarrow cosx\ne-1\Leftrightarrow x\ne-\pi+k2\pi\)

3.

Hàm số xác định khi \(cosx-cos3x\ne0\Leftrightarrow sin2x.sinx\ne0\Leftrightarrow\left[{}\begin{matrix}x\ne k\pi\\x\ne\dfrac{k\pi}{2}\end{matrix}\right.\)

Ta có \(-x^2+3x\) xác định với mọi \(x>0\)

\(x-1\ne0;\forall x\le0\Rightarrow\dfrac{2x-3}{x-1}\) xác định với mọi \(x\le0\)

\(\Rightarrow\) Hàm xác định với mọi x thuộc R hay \(D=R\)

TXĐ: \(D=R\)

\(y=x^3-2x^2+x-1\\ \Rightarrow y'=3x^2-4x+1\)

\(y'=0\Leftrightarrow3x^2-4x+1=0 \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{3}\\x=1\end{matrix}\right.\)

Bảng biến thiên:

d, Hàm số xác định khi:

\(\left\{{}\begin{matrix}cos\left(x+\dfrac{\pi}{4}\right)\ne0\\sinx.cosx+cos2x-3\ne0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x+\dfrac{\pi}{4}\ne\dfrac{\pi}{2}+k\pi\\\dfrac{1}{2}sin2x+cos2x\ne3\end{matrix}\right.\)

\(\Leftrightarrow x\ne\dfrac{\pi}{4}+k\pi\)

e, Hàm số xác định khi:

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