Question

The domain of tan^-1 (2x + 1) is
(a) R. (b) R-{1/2} ., (C) R-{-1/2} , (d) None of these​

Answer 1

The domain of $\sf{ { \tan}^{ - 1}(2x + 1) }$ is R

Given :

The function $\sf{ { \tan}^{ - 1}(2x + 1) }$

To find :

The domain of $\sf{ { \tan}^{ - 1}(2x + 1) }$ is

(a) R

(b) R - {1/2}

(c) R - { - 1/2}

(d) None of these

Solution :

Step 1 of 2 :

Write down the given function

The function is $\sf{ { \tan}^{ - 1}(2x + 1) }$

Step 2 of 2 :

Find the domain of the function

We know that $\sf{ { \tan}^{ - 1}x }$ is well defined when

$\sf - \infty < x < + \infty$

Thus we can say that $\sf{ { \tan}^{ - 1}(2x + 1) }$ is well defined when

$\sf - \infty < 2x + 1 < + \infty$

$\displaystyle \sf{ \implies } - \infty < x < + \infty$

$\displaystyle \sf{ \implies x \in \: R}$

So domain of $\sf{ { \tan}^{ - 1}(2x + 1) }$ is R

Hence the correct option is (a) R