Chapter 4.3, Problem 2QR

To determine

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

Answer to Problem 2QR

  $\begin{array}{l}Domain=[-1,1]\\ Range=\left[0,\pi \right]\\ {\mathrm{Cos}}^{-1}(1)=0\end{array}$

Explanation of Solution

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

Graph:

  

Interpretation:

In the above graph it is clear that the domain is [-1,1] and range $\left[0,\pi \right]$

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

  $\begin{array}{l}{\cos }^{-1}(1)=\text{An}\text{angle}\text{in}\left[0,\pi \right]\text{whose}\text{cosine}\text{is}1\\ {\cos }^{-1}(1)=0\end{array}$