The domain of f(x) = sin⁻¹(x² − 3x + 2) is:

The domain of f(x) = sin⁻¹(x² − 3x + 2) is:

• A. [0, 2]
• B. [1, 2]
• C. [(3−√5)/2, (3+√5)/2]
• D. [0, 1] ∪ [2, 3]

Answer: C) [(3−√5)/2, (3+√5)/2]

Explanation: For sin⁻¹(y), −1 ≤ y ≤ 1. Solve −1 ≤ x² − 3x + 2 ≤ 1. x² − 3x + 2 ≤ 1 → x² − 3x + 1 ≤ 0 → x ∈ [(3−√5)/2, (3+√5)/2]. x² − 3x + 2 ≥ −1 → x² − 3x + 3 ≥ 0, discriminant negative so always true. Domain is [(3−√5)/2, (3+√5)/2].