Question

Find the domain of the function $f\left(x\right)=\frac{1}{\left[x\right]-5}.$
Where [.] denotes GIF.

Answer 1

The function $f\left(x\right)=\frac{1}{\left[x\right]-5}$ is well defined iff:
$\left[x\right]-5\ne 0$
$\Rightarrow \left[x\right]\ne 5$
$\Rightarrow x\notin [5,6)$
$\Rightarrow x\in R-[5,6)$