Final answer:
The x value of the removable discontinuity in the function f(x) = ((3x - 4)(x + 2)(x - 2))/((3x - 1)(x + 2)) is x = -2. This occurs because the factor (x + 2) cancels out upon simplification of the function, which removes the discontinuity.
Step-by-step explanation:
To find the x value of the removable discontinuity in the function f(x) = ((3x - 4)(x + 2)(x - 2))/((3x - 1)(x + 2)), we must analyze the factors of the numerator and the denominator of the function. A removable discontinuity occurs when the same factor is present in both the numerator and the denominator, and it cancels out.
Here, the factor (x + 2) is in both the numerator and the denominator. This suggests a potential discontinuity at x = -2. However, the discontinuity is removable because we can simplify the function by canceling out the (x + 2) factors:
f(x) = ((3x - 4)(x - 2))/(3x - 1)
After simplification, the function is continuous at x = -2, so there is no actual discontinuity in the simplified function, which means x = -2 is a removable discontinuity for the original function.