Question

The domain of sin^-1(log₃(x/3)) is

(a) [1, 9]

(b) [-1, 9]

(c) [-9, 1]

(d) [-9, -1]

Answer 1

Correct option (a) [1, 9]

Explanation:

As we know that, domain of sin^-1x is [-1, 1]

Therefore, -1 ≤ log₃(x/3)≤ 1

⇒ 3^-1 ≤ (x/3) ≤ 3

⇒ 1/3 ≤ (x/3) ≤ 3

⇒ 1 ≤ x ≤ 9

Thus the domain of f(x) is [1, 9]