Question

1)tìm tập xác định:

a) Y=\(\frac{\sqrt{3-2x}}{\sqrt{1-x}}+\frac{\sqrt{2x+1}}{x}\)

b)Y=\(\frac{\sqrt{3x+5}}{x-2}+\frac{\sqrt{2x+3}}{\sqrt{4-x}}\)

Answer 1

a) \(Y=\frac{\sqrt{3-2x}}{\sqrt{1-x}}+\frac{\sqrt{2x+1}}{x}\)

\(\Rightarrow\left\{{}\begin{matrix}3-2x\ge0\\1-x>0\\2x+1\ge0\\x\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\le\frac{3}{2}\\x< 1\\x\ge\frac{-1}{2}\\x\ne0\end{matrix}\right.\)

TXĐ: \([-\frac{1}{2};\frac{3}{2}]\backslash\left\{0\right\}\)

b) \(Y=\frac{\sqrt{3x+5}}{x-2}+\frac{\sqrt{2x+3}}{\sqrt{4-x}}\)

\(\left\{{}\begin{matrix}3x+5\ge0\\x-2\ne0\\2x+3\ge0\\4-x>0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge-\frac{5}{3}\\x\ne2\\x\ge-\frac{3}{2}\\x< 4\end{matrix}\right.\)

TXĐ: \([-\frac{5}{3};4)\backslash\left\{2\right\}\)