Final answer:
The correct value of cos(2x) using the double-angle formula and given that cos x = 2/3 and x is in Quadrant I is -1/9; however, this is not an option provided. There may be an error in the question or the given options.
Step-by-step explanation:
To find the exact value of cos(2x) when cos x = 2/3 and x is in Quadrant I, we can use the double-angle formula for cosine, which is cos(2x) = cos^2(x) - sin^2(x). Alternatively, we can use the identity cos(2x) = 2cos^2(x) - 1. Since cos x = 2/3, we have:
cos(2x) = 2(2/3)^2 - 1 = 2(4/9) - 1 = 8/9 - 1 = 8/9 - 9/9 = -1/9
However, the options provided do not include -1/9, and there may be an error in the formulation of the question or in the options. If we were obliged to choose from the provided options, we'd need more information or a correction to the question.