Chapter 4.3, Problem 5QR

To determine

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

Answer to Problem 5QR

  $\begin{array}{l}\text{Domain}=R\\ \text{Range}=R\\ \tan ({\tan }^{-1}(1))=1\end{array}$

Explanation of Solution

Given information: Given function $y=\tan ({\tan }^{-1}x)$

Graph:

  

Interpretation:

In the above graph it is clear that the domain is real number and range is also real number.

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

  $\begin{array}{l}y=\tan ({\tan }^{-1}x)\\ y=x\\ \text{at}x=1\\ y=1\end{array}$