Chapter 3.3, Problem 44E

To determine

To state : true or false.

Answer to Problem 44E

FALSE

Explanation of Solution

Given information :

The domain of function $y={\tan }^{-1}x$ is $-1\le x\le 1$ .

Since, the domain and range of $y=\tan x$ is $ℝ-\frac{\left(2n+1\right)\pi }{2}:n\in \mathbb{Z}$ and $ℝ$ respectively.

In inverse case of trigonometric function, the range become domain for inverse function.

Thus, domain of function $y={\tan }^{-1}x$ is $ℝ$ .

Hence, the statement is false.