The range of the function $f\left(x\right)={\tan }^{-1}\left[x\right],-\frac{\pi }{4}\le x\le \frac{\pi }{4}$ where $\left[.\right]$ deonotes the greatest integer functiontion

$\begin{array}{l}f\left(x\right)={\tan }^{-1}\left[x\right]\\ If\frac{-\pi }{4}\le x\le \frac{\pi }{4}\\ \Rightarrow -0.78\le x\le 0.78\\ \therefore \left[x\right]=\{-1,0\}\\ Range=\{f(-1),f\left(0\right)\}=\{{\mathrm{Tan}}^{-1}(-1),{\tan }^{-1}\left(0\right)\}\\ \Rightarrow \{-\frac{\pi }{4},0\}\end{array}$