Question

Tìm tập xác định của các hàm số sau:

1) y =\(\dfrac{2x^2-2}{\left|x^{^2}-4\right|+\left|x+2\right|}\)

2) y = \(\dfrac{3x-2}{\left|x-2\right|-\left|x+1\right|}\)

3) y = \(\dfrac{\sqrt{x^{^2}+10}-\sqrt{2x+11}}{\left|3x-2\right|-4}\)

4) y = \(\dfrac{x^{^3}-3}{\sqrt{x-2}-\sqrt{7-3x}}\)

Answer 1

1: ĐKXĐ: \(\left|x^2-4\right|+\left|x+2\right|< >0\)

\(\Leftrightarrow x\ne-2\)

2: ĐKXĐ: \(\left|x-2\right|-\left|x+1\right|< >0\)

\(\Leftrightarrow\left|x-2\right|< >\left|x+1\right|\)

\(\Leftrightarrow\left\{{}\begin{matrix}x-2< >x+1\\x-2< >-x-1\end{matrix}\right.\Leftrightarrow2x< >1\Leftrightarrow x< >\dfrac{1}{2}\)

3: ĐKXĐ: \(\left\{{}\begin{matrix}2x+11>=0\\\left\{{}\begin{matrix}3x-2< >4\\3x-2< >-4\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>=-\dfrac{11}{2}\\x\notin\left\{2;-\dfrac{2}{3}\right\}\end{matrix}\right.\)