Question

The domain of the function $f\left(x\right)=\frac{7}{\left[|x|\right]-5}$ is
(where $[.]$ denotes the greatest integer function)

Answer 1

$f\left(x\right)=\frac{7}{\left[|x|\right]-5}$
For function to be defined,
$\left[|x|\right]-5\ne 0\Rightarrow \left[|x|\right]\ne 5\Rightarrow |x|\notin [5,6)\Rightarrow x\notin (-6,-5]\cup [5,6)$
$\therefore$Domain of $f\left(x\right)=R-(-6,-5]\cup [5,6)$