Answer:
The maximum value of the function f(x) = -2 sin(3 x - pi) + 7 is 9, and the minimum value is 5.
Step-by-step explanation: The function f(x) = -2 sin(3 x - pi) + 7 is a sinusoidal function with an amplitude of 2, a period of 2π/3, a phase shift of π/3 to the right, and a vertical shift of 7 units up.
To find the maximum and minimum values of the function, we need to find the maximum and minimum values of the sinusoidal part of the function, which is -2 sin(3 x - pi). The maximum value of sin(3 x - pi) is 1, and the minimum value is -1. Therefore, the maximum value of -2 sin(3 x - pi) is -2 times the minimum value of sin(3 x - pi), which is -2(-1) = 2. The minimum value of -2 sin(3 x - pi) is -2 times the maximum value of sin(3 x - pi), which is -2(1) = -2.
To find the maximum and minimum values of the function f(x) = -2 sin(3 x - pi) + 7, we need to add 7 to the maximum and minimum values of -2 sin(3 x - pi). Therefore, the maximum value of f(x) is 7 + 2 = 9, and the minimum value of f(x) is 7 - 2 = 5.