Mathematics - Functions Question with Solution | TestHub

Given:

$f\left(x\right)=\frac{1}{\sqrt{{\left[x\right]}^2-3\left[x\right]-10}}$

For $f\left(x\right)$ to be defined,

${\left[x\right]}^2-3\left[x\right]-10>0$

$\Rightarrow \left(\left[x\right]-5\right)\left(\left[x\right]+2\right)>0$

$\Rightarrow \left[x\right]<-2 \& \left[x\right]>5$

$\Rightarrow x<-2 \& x\ge 6$

So, domain is $\left(-\infty ,-2\right)\cup [6,\infty )$.