Final answer:
Yes, the expression (1/2x - 4) can have an inverse since it represents a simple linear function. The inverse can be found by expressing x in terms of y, resulting in x = 2y + 8.
Step-by-step explanation:
The expression (1/2x - 4) can have an inverse if we treat it as a function, f(x) = 1/2x - 4, which is a simple linear function. To find the inverse of a function, we essentially solve for the input x given an output y. This requires expressing x in terms of y, ensuring that for every unique input there is a unique output and vice versa. The inverse of f(x) = 1/2x - 4 is found by setting y = 1/2x - 4, then solving for x to get x = 2y + 8. Since there are no restrictions that would cause this function to not have an inverse (it is a continuous, one-to-one function across all real numbers), the answer to this question is A. Yes, (1/2x - 4) has an inverse.