Question

The domain of sin^-1⁡(3x) is equal to _______

(a) [-1, 1]

(b) \([\frac{-1}{3}, \frac{1}{3}]\)

(c) [-3, 3]

(d) [-3π, 3π]

I have been asked this question in exam.

My question is taken from Inverse Trigonometric Functions Basics topic in chapter Inverse Trigonometric Functions of Mathematics – Class 12

Answer 1

Correct choice is (b) \([\frac{-1}{3}, \frac{1}{3}]\)

The explanation: The domain of y=sin^-1⁡x is -1≤x≤1.

∴the domain of y=sin^-1⁡3x is-1≤3x≤1

⇒ \([\frac{-1}{3} ≤ x ≤ \frac{1}{3}]\)

Hence, \([\frac{-1}{3}, \frac{1}{3}]\).