Answer
a. $(-\infty, \infty) $
b. $(-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2})$
c. increasing
d. no
Work Step by Step
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.
