question_answer

Domain of definition of the function \[f(x)=\frac{3}{4-{{x}^{2}}}+{{\log }_{10}}({{x}^{3}}-x),\] is

A) \[(-1,0)\cup (1,2)\cup (2,\infty )\]  

B) \[(a,2)\]

C) \[(-1,0)\cup (a,2)\]

D)        \[(1,2)\cup (2,\infty )\]

Correct Answer: A

Solution :

[a] \[f(x)=\frac{3}{4-{{x}^{2}}}+{{\log }_{10}}({{x}^{3}}-x)\] \[4-{{x}^{2}}\ne 0;\,\,{{x}^{3}}-x>0;\] \[x\ne \pm \sqrt{4}\] and \[-1<x<0\] or \[1<x<\infty \] \[\therefore D=(-1,0)\cup (1,\infty )-\{\sqrt{4}\}\] \[D=(-1,0)\cup (1,2)\cup (2,\infty )\]