Question

Tìm tập xác định của các hàm số sau:

1. y = \(\frac{\sqrt{x-1}+\sqrt{4-x^2}}{\left(x-2\right)\left(x+3\right)}\)

2. y = \(\frac{\sqrt{2-x}}{x^2-5x+4}\)

3. y = \(-\frac{\sqrt{2-3x}}{\sqrt{1+2x}}\)

Answer 1

ĐKXĐ:

a/ \(\left\{{}\begin{matrix}x\ge1\\4-x^2\ge0\\x\ne2\\x\ne-3\end{matrix}\right.\) \(\Rightarrow1\le x< 2\)

b/ \(\left\{{}\begin{matrix}2-x\ge0\\x^2-5x+4\ne0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x\le2\\x\ne1\\x\ne5\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x\le2\\x\ne1\end{matrix}\right.\)

c/ \(\left\{{}\begin{matrix}2-3x\ge0\\1+2x>0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x\le\frac{2}{3}\\x>-\frac{1}{2}\end{matrix}\right.\) \(\Rightarrow-\frac{1}{2}< x\le\frac{2}{3}\)