question_answer

Domain of definition of the function \[f(x)=\frac{3}{4-{{x}^{2}}}+{{\log }_{10}}({{x}^{3}}-x)\], is     AIEEE  Solved  Paper-2003

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