✔ 最佳答案
The answer is D. 13
-1 <= sin(3x) <= 1
-2 <= 2sin(3x) <= 2
-3 <= 2sin(3x)-1 <= 1
When 2sin(3x)-1 is negative, the minimum is -3,it turns 9 after squaring.
When 2sin(3x)-1 is positive, the maximum is 1,it turns 1 after squaring.
Therefore, the greatest value of (2sin(3x)-1)^2+4 is (-3)^2+4 = 9+4 = 13