The domain of the definition of the function $f(x)=\frac{1}{4-x^{2}}+ \log_{10}(x^{3}-x)$  is : Option 1) $(-1,0)\cup (1,2)\cup (3,\infty )$ Option 2) $(-2,-1)\cup (-1,0)\cup (2,\infty )$ Option 3) $(-1,0)\cup (1,2)\cup (2,\infty )$ Option 4) $(1,2)\cup (2,\infty )$

$\\f(x)=\frac{1}{4-x^{2}}+\log_{10}(x^{3}-x)\\\\\\\:(4-x^{2} )\neq 0\\\\\\\:(2-x)(2+x) \neq 0\\\\\\\:$

$x\neq 2,-2$

$x\epsilon R-\left \{ 2,-2 \right \}$

$(x^{3}-x)\:\:so$                                                 $\downarrow$

$=x(x^{2}-1)$

$=x(x+1)(x-1)>0$

$x\epsilon (-1,0)\cup (1,2)\cup (2,\infty )$

Domain :  $x\epsilon (-1,0)\cup (1,2)\cup (2,\infty )$

Option 1)

$(-1,0)\cup (1,2)\cup (3,\infty )$

Option 2)

$(-2,-1)\cup (-1,0)\cup (2,\infty )$

Option 3)

$(-1,0)\cup (1,2)\cup (2,\infty )$

Option 4)

$(1,2)\cup (2,\infty )$

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