\[\begin{array}{l}
a)\,\,\,\sqrt {3 - x} + \frac{4}{{{x^2} - 1}}\\
DK:\,\,\,\,\left\{ \begin{array}{l}
3 - x \ge 0\\
{x^2} - 1 \ne 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x \le 3\\
x \ne \pm 1
\end{array} \right..\\
\Rightarrow D = \left( { - \infty ;\,\,3} \right]\backslash \left\{ { \pm 1} \right\}.\\
b)\,\,\,y = 2\sqrt {1 - x} - \frac{1}{x}\\
DK:\,\,\,\left\{ \begin{array}{l}
1 - x \ge 0\\
x \ne 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x \le 1\\
x \ne 0
\end{array} \right.\\
\Rightarrow D = \left( { - \infty ;\,\,1} \right]\backslash \left\{ 0 \right\}.\\
c)\,\,\,\frac{3}{{\sqrt {4x - {x^2}} }}\\
DK:\,\,\,4x - {x^2} > 0\\
\Leftrightarrow {x^2} - 4x < 0\\
\Leftrightarrow x\left( {x - 4} \right) < 0\\
\Leftrightarrow 0 < x < 4.\\
\Rightarrow D = \left( {0;\,\,\,4} \right).
\end{array}\]
