Question

If $f\left(x\right)=\sqrt{4-x^2}+\frac{1}{\sqrt{|sinx|-sinx}}$, then the domain of f(x) is

• A. [–2, 0]
• B. (0, 2]
• C. [–2, 2}
• D. [–2, 0)

Answer 1

The correct option is D [–2, 0)

$f\left(x\right)=\sqrt{4-x^2}+\frac{1}{\sqrt{|sinx|-sinx}}$
(i) $4-x^2\ge 0x^2\le 4\Rightarrow -2\le x\le 2$
(ii) |sin x| - sin x > 0
when sin x < 0, |sin x| = - sin x $\Rightarrow$ -2 sin x>0 $\Rightarrow$ sin x<0 if |sin x| = sin x then 0>0 not possible
$\therefore$ Domain is [-2,0)