Find the Domain of the Function
The domain of the function
\[ f(x)=\frac1{\sqrt{x-|x|}} \]
is
(a) \(R_0\)
(b) \(R^+\)
(c) \(R^-\)
(d) none of these
Since square root is in denominator,
\[ x-|x|>0 \]
Case I: \(x\ge0\)
\[ |x|=x \]
\[ x-|x|=x-x=0 \]
Not allowed.
Case II: \(x<0\)
\[ |x|=-x \]
\[ x-|x|=x-(-x)=2x \]
Since \(x<0\),
\[ 2x<0 \]
Not allowed.
Therefore, no real value satisfies the condition.
Domain:
\[ \phi \]
Hence,
\[ \boxed{\text{Correct Answer: (d)}} \]