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

Answers (1)

A Aadil.Khan

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

$x\neq 2,-2$

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

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

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

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

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

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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