Question

If f(x) = √4 - x² + (1/√|sin x|- sin x), then the domain of f(x) is

(A)  (−2, 0)

(B)  (0, 2)

(C)  (−2, 2)

(D)  [−2, 0)

Answer 1

Correct option   (D) [−2, 0)

Explanation :

We have

(i)  Here, 4 - x² ≥ 0 ⇒ x² ≤ 4 ⇒ -2 ≤ x ≤ 2.

(ii)  Here, |sinx| - sinx > 0.  

When sinx < 0, we have |sinx| = -sinx ⇒ -2sinx > 0 ⇒ sinx < 0 if |sinx| = sinx 

Then, we get 0 > 0, which is not possible. Therefore, the domain is [-2, 0).