Find the Domain of the Function
Question:
The domain of definition of the function
\[ f(x)=\sqrt{\frac{x-2}{x+2}}+\sqrt{\frac{1-x}{1+x}} \]
is
(a) \((-\infty,-2]\cup[2,\infty)\)
(b) \([-1,1]\)
(c) \(\phi\)
(d) none of these
Solution:
For the first square root,
\[ \frac{x-2}{x+2}\ge0 \]
\[ x\in(-\infty,-2)\cup[2,\infty) \]
For the second square root,
\[ \frac{1-x}{1+x}\ge0 \]
\[ x\in(-1,1] \]
There is no common value of \(x\).
Therefore, domain is
\[ \phi \]
\[ \boxed{\text{Correct Answer: (c)}} \]