Question

The domain of the function $f\left(x\right)=\frac{1}{\sqrt{x+|x|}},$ is

• A. $(1,\infty )$
• B. $(-\infty ,0)$
• C. $(0,\infty )$
• D. $(\sqrt{2},\infty )$

Answer 1

The correct option is C $(0,\infty )$

Given,
$f\left(x\right)=\frac{1}{\sqrt{x+|x|}}$

We know that
$x+|x|=\{\begin{array}{c}2x,\text{if}x>0\\ 0,\text{if}x\le 0\end{array}$

For $f\left(x\right)$ to be defined,
$x+|x|>0$
$\Rightarrow x>0$
$\therefore x\in (0,\infty )$

Hence, domain of the function is $(0,\infty ).$