Precalculus (6th Edition)

a. $(-\infty, \infty)$ b. $(-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2})$ c. increasing d. no
See figure $20$ on p.$702.$ (or the table on page 703 ) In order to have an inverse, the domain of $\tan x$ is restricted to .$(-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2})$. $y=\tan^{-1} x$ ($y$ is the number from $(-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2})$ for which $\tan y=x$) (a) and (b) Domain: $(-\infty, \infty)$ Range:$(-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2})$ Quadrants (unit circle): I and IV (c) Figure $20$: $\tan^{-1}x$ is increasing. For part (d), see the domain. All real numbers are in the domain. There is no x for which $\tan^{-1}x$ is not defined.