The domain of the definition of the function $f(x)=\frac{1}{4-x^2}+\log _{10}\left(x^3-x\right)$ is

Question

Aicharya · Accepted Answer

$f(x)=\frac{1}{4-x^2}+\log _{10}\left(x^3-xight)$ to define $f(x) 4-x^2 
eq 0$ and $x^3-x>0$ $\Rightarrow x^2 
eq 4 	ext { and } x(x-1)(x+1)>0$ $\Rightarrow x 
eq \pm 2$ and $\Rightarrow x \in(-1,0) \cup(1,2) \cup(2, \infty)$

The domain of the definition of the function $f(x)=\frac{1}{4-x^2}+\log _{10}\left(x^3-x\right)$ is

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