Final answer:
The domain of the composite function f(g(x)), where f(x) = 2x - 5 and g(x) = x² - 3x, is all real numbers since both functions are unconstrained polynomial expressions. Therefore, none of the given options A to D is correct.
Step-by-step explanation:
To determine which of the following is the domain of f(g(x)): A) x≤−2, B) x≥5, C) x≤0, D) x≥3, we need to look at the composition of the two functions f(x) and g(x), where f(x) = 2x - 5 and g(x) = x² - 3x. Since the function f(x) is a linear function and does not have any restrictions on its domain, the domain of f(g(x)) is solely dependent on the domain of g(x), which is also unrestricted since it is a polynomial.
As g(x) doesn't have restrictions on its values, the domain for f(g(x)) is thus all real numbers. This is because there are no fractions, square roots, or logarithms that could impose restrictions on the domain. Hence, none of the options A, B, C, or D are needed to describe the domain of the composite function f(g(x)).