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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»

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



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