Question

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

Answer 1

Let $f\left(x\right)=\frac{1}{\sqrt{x-\left[x\right]}}$

For $f\left(x\right)$ to exist

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

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

$\Rightarrow$$x$ is a negative real number

Therefore the domain of the function is the set of negative real numbers

and range is the set of positive real numbers