Question

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

Answer 1

We have,
$f\left(x\right)=\sqrt{\left[x\right]-x}$
We know that $0\le x-\left[x\right]<1$ for all $xϵR$
$\Rightarrow \sqrt{x-\left[x\right]}$ is defined for all $xϵR$.
$\therefore$ Domain (f) = R
and Range (f) = [0,1)