Answer
a. $[-1, 1] $
b. $[-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2}]$
c. increasing
d. because $-2$ is not in the range of $\sin x$
Work Step by Step
See figure 14 on p.699
(or the table on page 703 )
$y=\sin^{-1}x$
($y$ is the number from $[-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2}]$ for which $\sin y=x$)
Domain: $[-1, 1] $
Range:$ [-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2}]$
Quadrants (unit circle): I and IV.
Figure 14: $\sin^{-1}x$ is increasing.
For part (d), the domain of the inverse function equals the range of the function. There is no y for which $\sin y=-2$, so $\sin^{-1}(-2) $is not defined.
a. $[-1, 1] $
b. $[-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2}]$
c. increasing
d. because $-2$ is not in the range of $\sin x$
