Final answer:
Option D). The largest integer value of x such that f(x) = g(x), based on the given domain of 1.5 ≤ x ≤ 4.5, is potentially 4. Without the functions' explicit forms, we cannot provide the exact value, but based on the domain, 4 is the largest integer within the range.
Step-by-step explanation:
You must compare the functional values of f(x) and g(x) throughout the domain defined by the inequality 1.5 ≤ x ≤ 4.5 in order to determine the greatest integer value of x such that f(x) = g(x). The precise value at which f(x) and g(x) are equal cannot be found without the explicit forms of these functions. If, on the other hand, you were given graphs or particular functional expressions of f(x) and g(x), you would solve for x inside the specified domain by setting f(x) equal to g(x).
Given that the largest integer value of x is between 1.5 and 4.5, we can consider the integers 2, 3, and 4. Of these, 4 is the largest and falls within the given domain. Thus, without additional information, the largest integer value of x that could potentially satisfy f(x) = g(x), based on the domain alone, would be 4.