Question

The domain of tan^-1 (2x + 1) is
(with calculation)

Answer 1

SOLUTION

TO DETERMINE

The domain of the function

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

EVALUATION

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

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

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

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

Hence the required Domain is

$\sf{ (- \infty \: , \: + \infty )}$

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