Relations and Functions — MATHS STD 11 Science — Question

1. $ \text{R}$

Solution:

Since $ \tan^1$ x exists if $\text{x}\in(-\infty,\infty)$

So, (2x + 1) is defined if

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

$\Rightarrow-\infty < \times <\infty$

$\Rightarrow \text{x}\in (-\infty,\infty)$

$\Rightarrow \text{x}\in \text{R}$

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