A) (1, 2)
B) \[(-1,0)\cup (1,2)\]
C) \[(1,2)\cup (2,\infty )\]
D) \[(-1,0)\cup (1,2,)\cup (2,\infty )\]
Correct Answer: D
Solution :
Since, \[f(x)=\frac{3}{4-{{x}^{2}}}+{{\log }_{10}}({{x}^{3}}-x)\] For domain of \[f(x),\] \[{{x}^{3}}-x>0\] \[\Rightarrow \] \[x\,(x-1)\,(x+1)>0\] Region is \[(-1,\,0)\cup (1,\infty )\] and \[4-{{x}^{2}}\ne 0\Rightarrow x\ne \pm 2\] Region is \[(-\infty ,-2)\cup (-2,2)\cup (2,\infty )\] \[\therefore \] Common region is \[(-1,0)\,\cup \,(1,\,2)\cup (2\,,\infty )\]You need to login to perform this action.
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