Question

The domain of the function $f\left(x\right)=\frac{1}{\sqrt{x-\left[x\right]}}$

• A. $R$
• B. $R-\left\{Z\right\}$
• C. $Z$
• D. none of these

Answer 1

The correct option is B $R-\left\{Z\right\}$

We have $f\left(x\right)=\frac{1}{\sqrt{x-|x|}}$

$\Rightarrow x-\left[x\right]>0$

$\Rightarrow x>\left[x\right]$ is defined only when $x\notin Z.$

Domain of $f\left(x\right)$ is $R-Z$