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 :
[c] f(x) is to be defined when \[{{x}^{2}}-1>0\] and \[3+x>0\] and \[3+x\ne 1.\] i.e., \[{{x}^{2}}>1\] and \[x>-3\] and \[x\ne -2\], i.e., \[x<-1\,\,or\,\,x>1\] and \[x>-3\,\,and\,\,x\ne -2\] \[\therefore {{D}_{f}}=(-3,-2)\cup (-2,-1)\cup (1,\infty )\]
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