A) \[R-[-1,\,1]\]
B) \[\{-\infty ,1\}\]
C) \[\{-\infty ,-1\}\cup (0,1)\]
D) None of the above
Correct Answer: C
Solution :
\[f(x)={{\left[ {{\left( \frac{x}{1-|x|} \right)}^{1/2}} \right]}^{\frac{1}{1001}}}\] \[f(x)\] is defined, if \[\frac{x}{1-|x|}>0\] ie, \[x>0,1-|x|>0\] and \[x<0,\,\,1-|x|<0\] \[\Rightarrow \] \[x>0,|x|<1\] and \[x<0,|x|>1\] \[\Rightarrow \] \[x\in (0,1)\] and \[x\in (-\infty ,-1)\] \[\therefore \] \[x\in (-\infty ,-1)\,\cup \,(0,1)\]
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