Question
Find the domain of function given by $: \text{f}\text{(x)}=\frac{1}{\sqrt{\text{x}+|\text{x}|}}$
✓
Answer
We have, $\text{f}\text{(x)}=\frac{1}{\sqrt{\text{x}+|\text{x}|}}$
If $x > 0, x + |x| = x + x = 2x > 0$
If $x < 0, x + |x| = x -x = 0$
Clearly$, x = 0$ is not possible.
$\therefore$ Domain of $f = R^+$
If $x > 0, x + |x| = x + x = 2x > 0$
If $x < 0, x + |x| = x -x = 0$
Clearly$, x = 0$ is not possible.
$\therefore$ Domain of $f = R^+$
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