question_answer

The domain of the definition of the function \[f(x)=\frac{1}{4-{{x}^{2}}}+{{\log }_{10}}({{x}^{3}}-x)\]is :-             [JEE Main 9-4-2019 Afternoon]

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

B) \[(-1,0)\cup (1,2)\cup (3,\infty )\]

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

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

Correct Answer: C

Solution :

\[4-{{x}^{2}}\ne 0;{{x}^{3}}-x>0\]           \[x=\pm 2\]   \[x(x-1)(x+2)>0\]                     \[\therefore \]\[{{D}_{f}}\in (-1,0)\cup (1,2)\cup (2,\infty )\]