Question

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

Answer 1

We have,
$f\left(x\right)=\sqrt{x-\left[x\right]}$
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)