Question

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

• A. $R-\{5,6\}$
• B. $R$
• C. $R-\left\{5\right\}$
• D. None of the above

Answer 1

The correct option is D None of the above

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