Question

The domain of the function $f\left(x\right)=ta{n}^{-1}\sqrt{\left[x\right]+[-x]}+\sqrt{2-|x|}+\frac{1}{x^2}$ is :
(where [.] is the greatest integer function)

Answer 1

$\begin{array}{c}\left[x\right]+\left[-x\right]\ge 0\\ \left[x\right]+\left[-x\right]=0\\ x\in I\\ \\ 2-\left|x\right|\ge 0\\ \left|x\right|\le 0\\ -2\le x\le 2\\ \\ \frac{1}{x^2}\ne \infty \\ x^2\ne 0\\ \\ commonis\\ x\in \left\{-2,-1,1,2\right\}\end{array}$