Problem 4 - Entrance Test

1. Domain: 3x - 2 ≥ 0 → x ≥ 2/3. 2. For x - 1 < 0 → always true since √(3x - 2) ≥ 0. So x < 1 → x ∈ [2/3,1). 3. For x - 1 ≥ 0 → square both sides: 3x - 2 > x² - 2x + 1 → 0 > x² -5x +3. Solve x² -5x +3 <0 → x ∈ ( (5 - √13)/2, (5 + √13)/2 ). 4. Total solution: x ∈ [2/3, (5 + √13)/2 ) ≈ [2/3, 3.30). Since options are approximate, best choice is B.