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