Mathematics - Functions Question with Solution | TestHub

$y={\tan }^{-1}\left(\frac{2}{\pi }{\tan }^{-1}x\right)$, $-1\le x\le 1$.

$$-\frac{\pi }{4}\le {\tan }^{-1}x\le \frac{\pi }{4}$$

$$-\frac{1}{2}\le \frac{2}{\pi }{\tan }^{-1}x\le \frac{1}{2}$$

$$-{\tan }^{-1}\frac{1}{2}\le {\tan }^{-1}\left(\frac{2}{\pi }{\tan }^{-1}x\right)\le {\tan }^{-1}\left(\frac{1}{2}\right)$$

Since $y=0$ is the only integer in this range, there is only one integer value.