The domain of the function $f(x)=\frac{1}{\sqrt{x+|x|}}$ is
The domain of the function $f(x)=\frac{1}{\sqrt{x+|x|}}$ is
$(-\infty, 0)$
$(2,5)$
$(0, \infty)$
$(-\infty, \infty)$
Solution
$f(x)=\frac{1}{\sqrt{x+|x|}}$
Here $x+|x| \geq 0$ and $\sqrt{x+|x|} \neq 0$
$\therefore \mathrm{x}+|\mathrm{x}|>0$
Now when $x>0, x+|x|=x+x \Rightarrow 2 x>0$.
When $\mathrm{x} < 0, \mathrm{x}+|\mathrm{x}|=\mathrm{x}-\mathrm{x}=0$
$\therefore \mathrm{x}>0$ is the required domain.