imo class 12 inverse trigonometric functions

The domain of f(x) = sin⁻¹(2x − 1) is:

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The domain of f(x) = sin⁻¹(2x − 1) is:

  • A. [0, 1]
  • B. [−1, 1]
  • C. [−1/2, 1/2]
  • D. [0, 2]

Answer: A) [0, 1]

Explanation: For sin⁻¹(y), y ∈ [−1, 1]. So −1 ≤ 2x − 1 ≤ 1 → 0 ≤ 2x ≤ 2 → 0 ≤ x ≤ 1. Domain is [0, 1].

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