A) \[(-3,-1)\cup (1,\infty )\]
B) \[(-3,-1)\cup [1,\infty )\]
C) \[(-3,-2)\cup (-2,-1)\cup (1,\infty )\]
D) \[[-3,-2)\cup (-2,-1)\cup [1,\infty )\]
Correct Answer: C
Solution :
\[f(x)\]is defined when \[{{x}^{2}}-1>0,\] \[\Rightarrow \] \[{{x}^{2}}>1\] \[\Rightarrow \] \[x<-1\]and \[x>1\] Also, \[3+x>0\]and \[x\ne -2\] \[\therefore \] \[x>-3\]and \[x\ne -2\] \[\therefore \]Domain \[=(-3,-2)\cup (-2,-1)\cup (1,\infty )\]
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