Question

The set of values of $x$ for which $\frac{1}{\sqrt{x+|x|}}$ is defined, is

• A. $(0,\infty )$
• B. $[0,\infty )$
• C. $R$
• D. $R-\left\{0\right\}$

Answer 1

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

$\frac{1}{\sqrt{x+|x|}}$ is defined when

$x+|x|>0$
So $x\ne 0$

When $x>0$
$x+|x|>0$
$\Rightarrow 2x>0\Rightarrow x>0$

When $x<0$
$x+|x|>0\Rightarrow x-x>0\Rightarrow 0>0$
Not possible.

Hence, $x\in (0,\infty )$