Question:
Write the domain of the real function $f(x)=\sqrt{[x]-x}$.
Solution:
$[x]$ is the greatest integer function.
$[x] \leq x, \forall x \in R$
$\Rightarrow[x]-x \leq 0, \forall x \in R$
$\Rightarrow \sqrt{[x]-x}$ does not exist for any $x \in R$.
Domain $=\phi$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.