Question

Domain of $f\left(x\right)=\sqrt{\left[x\right]+[-x]}$ . Where [.] denotes GIF.

Answer 1

We know that $\left[x\right]+[-x]=(\begin{array}{c}0,x\in Z\\ -1,x\notin Z\end{array}$

$\left[x\right]+[-x]$ results a negative value for $x\notin Z$

Also, the square root of a negative number is not a real number.

Hence, to have a real value for $\sqrt{\left[x\right]+[-x]},y\in Z.$

This includes $Z^{+}$, $Z^{-}\text{and 0}$.