The function you provided appears to have errors. Assuming it is f(x) = 4 - 2sin(x), and we are looking for minimum value; sine values oscillate from -1 to +1, thus -2sin(x) oscillates from -2 to +2. Therefore, the minimum value would occur when sin(x) has its maximum value of +1, rendering the expression as: 4 - 2(1) = 2. Thus the minimum value is 2. For the original query to contain a variable x outside the trigonometric function requires calculus to find the minimum.