3.

\(y=\dfrac{1-sin^24x}{5}=\dfrac{cos^24x}{5}\)

\(cos4x\in\left[-1;1\right]\Rightarrow cos^24x\in\left[0;1\right]\Rightarrow y\in\left[0;\dfrac{1}{5}\right]\Rightarrow\left\{{}\begin{matrix}y_{min}=0\\y_{max}=\dfrac{1}{5}\end{matrix}\right.\)

6.

\(y=sinx+cosx+2=\sqrt{2}sin\left(x+\dfrac{\pi}{4}\right)+2\)

\(sin\left(x+\dfrac{\pi}{4}\right)\in\left[-1;1\right]\Rightarrow y=\sqrt{2}sin\left(x+\dfrac{\pi}{4}\right)+2\in\left[-\sqrt{2}+2;\sqrt{2}+2\right]\)

\(\Rightarrow y_{min}=-\sqrt{2}+2\)

\(y_{max}=\sqrt{2}+2\)

1.

\(sin2x\in\left[-1;1\right]\Rightarrow y=3-2sin2x\in\left[1;5\right]\)

\(\Rightarrow\left\{{}\begin{matrix}y_{min}=1\\y_{max}=5\end{matrix}\right.\)

1, Hàm số xác định 

⇔ cos²x ≠ 4

Mà 0 ≤ cos²x ≤ 1 nên điều trên đúng ∀ x ∈ R

Tập xác định : D = R

2, Hàm số xác định ⇔ \(\left\{{}\begin{matrix}cos3x\ne0\\cosx\ne0\end{matrix}\right.\)

⇔ cos3x ≠ 0

⇔ x ≠ \(\pm\dfrac{\pi}{6}+k.\dfrac{\pi}{3}\) , k ∈ Z

Tập xác định : D = R \ { \(\pm\dfrac{\pi}{6}+k.\dfrac{\pi}{3}\) , k ∈ Z}

3, D = [- 2 ; 2]

4, D = [- 1 ; +\(\infty\)) \ {0 ; 4}

11, sin²x - cos²x ≠ 0 

⇔ cos2x ≠ 0

e: Ta có: \(2x\left(x-5\right)-26=x\left(2x+3\right)\)

\(\Leftrightarrow2x^2-10x-26-2x^2-3x=0\)

\(\Leftrightarrow-13x=26\)

hay x=-2

f: Ta có: \(x^2-9=-2x\left(x-3\right)\)

\(\Leftrightarrow\left(x-3\right)\left(x+3\right)+2x\left(x-3\right)=0\)

\(\Leftrightarrow\left(x-3\right)\left(3x+3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-1\end{matrix}\right.\)

g: Ta có: \(4x^3-9x=0\)

\(\Leftrightarrow x\left(2x-3\right)\left(2x+3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{3}{2}\\x=-\dfrac{3}{2}\end{matrix}\right.\)

h: Ta có: \(x^2-8x+2\left(x-8\right)=0\)

\(\Leftrightarrow\left(x-8\right)\left(x+2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=8\\x=-2\end{matrix}\right.\)

e. \(2x\left(x-5\right)-26=x\left(3+2x\right)\)

\(\Leftrightarrow2x^2-10x-26=3x+2x^2\)

\(\Leftrightarrow2x^2-10x-3x-2x^2=26\)

\(\Leftrightarrow-13x=26\) \(\Leftrightarrow x=-2\)

g. \(4x^3-9x=0\)

\(\Leftrightarrow x\left(4x^2-9\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\4x^2-9=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=0\\x^2=\dfrac{9}{4}\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\pm\dfrac{3}{2}\end{matrix}\right.\)

i. \(x^3-5x=0\)

\(\Leftrightarrow x\left(x^2-5\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x^2-5=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=0\\x^2=5\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\pm\sqrt{5}\end{matrix}\right.\)

k. \(x^2=10x-25\)

\(\Leftrightarrow x^2-10x+25=0\)

\(\Leftrightarrow\left(x-5\right)^2=0\)

\(\Leftrightarrow x-5=0\)

\(\Leftrightarrow x=5\)

f. \(x^2-9=-2x\left(x-3\right)\)

\(\Leftrightarrow\left(x-3\right)\left(x+3\right)=-2x\left(x-3\right)\)

\(\Leftrightarrow x+3=-2x\)

\(\Leftrightarrow3x=-3\)

\(\Leftrightarrow x=-1\)

h. \(x^2-8x+2\left(x-8\right)=0\)

\(\Leftrightarrow x\left(x-8\right)+2\left(x-8\right)=0\)

\(\Leftrightarrow\left(x-8\right)\left(x+2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-8=0\\x+2=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=8\\x=-2\end{matrix}\right.\)

j. \(x\left(x-5\right)-x+5=0\)

\(\Leftrightarrow x\left(x-5\right)-\left(x-5\right)=0\)

\(\Leftrightarrow\left(x-5\right)\left(x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-5=0\\x-1=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=1\end{matrix}\right.\)

l. \(2x^3-72x=0\)

\(\Leftrightarrow2x\left(x^2-36\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x^2-36=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=0\\x^2=36\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\pm6\end{matrix}\right.\)

1.

\(D=R\backslash\left\{\dfrac{\pi}{6}+\dfrac{k\pi}{3}\right\}\) là miền đối xứng

\(f\left(-x\right)=\left(-x^3-x\right)tan\left(-3x\right)=\left(x^3+x\right)tan3x=f\left(x\right)\)

Hàm chẵn

2.

\(D=R\)

\(f\left(-x\right)=\left(-2x+1\right)sin\left(-5x\right)=\left(2x-1\right)sin5x\ne\pm f\left(x\right)\)

Hàm không chẵn không lẻ 

3.

\(D=R\backslash\left\{\dfrac{\pi}{6}+\dfrac{k\pi}{3}\right\}\) là miền đối xứng

\(f\left(-x\right)=tan\left(-3x\right).sin\left(-5x\right)=-tan3x.\left(-sin5x\right)=tan3x.sin5x=f\left(x\right)\)

Hàm chẵn

4.

\(D=R\)

\(f\left(-x\right)=sin^2\left(-2x\right)+cos\left(-10x\right)=sin^22x+cos10x=f\left(x\right)\)

Hàm chẵn

5.

\(D=R\backslash\left\{k\pi\right\}\) là miền đối xứng

\(f\left(-x\right)=\dfrac{-x}{sin\left(-x\right)}=\dfrac{-x}{-sinx}=\dfrac{x}{sinx}=f\left(x\right)\)

Hàm chẵn