cos⁻¹(4x³ − 3x) = 3 cos⁻¹x holds for:
cos⁻¹(4x³ − 3x) = 3 cos⁻¹x holds for:
- A. x ∈ [−1, 1]
- B. x ∈ [1/2, 1]
- C. x ∈ [−1/2, 1/2]
- D. x ∈ [0, 1]
Answer: B) x ∈ [1/2, 1]
Explanation: Identity cos 3θ = 4cos³θ − 3cos θ. Put θ = cos⁻¹x, then x = cos θ. cos⁻¹(4x³−3x) = cos⁻¹(cos 3θ) = 3θ if 3θ ∈ [0,π] → θ ∈ [0,π/3]. So cos⁻¹x ∈ [0,π/3] → x ∈ [1/2, 1].
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