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  4. The domain of f(x)=(x/16 - x2)+(l o g)2(x3 - 2 x) is

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Q. The domain of $f\left(x\right)=\frac{x}{16 - x^{2}}+\left(l o g\right)_{2}\left(x^{3} - 2 x\right)$ is

NTA AbhyasNTA Abhyas 2020

Solution:

$16-x^{2}\neq 0$ and $x^{3}-2x>0$
$x\neq 4,-4\ldots ..\left(i\right)$
and $x\left(x^{2} - 2\right)>0$
$x\left(x + \sqrt{2}\right)\left(x - \sqrt{2}\right)>0$
Solution
$x\in \left(- \sqrt{2} , 0\right)\cup\left(\sqrt{2} , \in fty\right)\ldots \left(i i\right)$
Taking intersection of $\left(i\right)\&\left(i i\right)$ , we get,
$x\in \left(- \sqrt{2} , 0\right)\cup\left(\sqrt{2} , 4\right)\cup\left(4 , \in fty\right)$