Chapter 4.3, Problem 1QR

To determine

To Find: The domain and range of the given function and value at $x=1$

Answer to Problem 1QR

  $\begin{array}{l}Domain=[-1,1]\\ Range=\left[\frac{-\pi }{2},\frac{\pi }{2}\right]\\ {\mathrm{Sin}}^{-1}(1)=\frac{\pi }{2}\end{array}$

Explanation of Solution

Given information: Given function $y={\sin }^{-1}x$

Graph:

  

Interpretation:

In the above graph it is clear that the domain is [-1,1] and range $\left[\frac{-\pi }{2},\frac{\pi }{2}\right]$

Also, value of ${\sin }^{-1}x$ at $x=1$ , we get

  $\begin{array}{l}{\sin }^{-1}(1)=\text{An}\text{angle}\text{in}\left[\frac{-\pi }{2},\frac{\pi }{2}\right]\text{whose}\text{sine}\text{is}1\\ {\sin }^{-1}(1)=\frac{\pi }{2}\end{array}$