Find the Domain of the Function
The domain of the function
\[ f(x)=\sqrt{\frac{(x+1)(x-3)}{x-2}} \]
is
(a) \([ -1,2)\cup[3,\infty)\)
(b) \(( -1,2)\cup[3,\infty)\)
(c) \([ -1,2]\cup[3,\infty)\)
(d) none of these
For square root function,
\[ \frac{(x+1)(x-3)}{x-2}\ge0 \]
Critical points are
\[ -1,\;2,\;3 \]
Using sign analysis,
\[ \frac{(x+1)(x-3)}{x-2}\ge0 \]
for
\[ [-1,2)\cup[3,\infty) \]
Note that \(x=2\) is excluded because denominator becomes zero.
Therefore,
\[ \boxed{[-1,2)\cup[3,\infty)} \]
\[ \boxed{\text{Correct Answer: (a)}} \]