Final answer:
The function h(x) as a composite function h(x) = f(g(x)) is composed of f(x) = x^3 + \frac{1}{x} and g(x) = 3x - 5.
Step-by-step explanation:
To express the function h(x) = (3x - 5)^3 + \frac{1}{3x - 5} as a composite function of the form h(x) = f(g(x)), we need to identify an inner function g(x) which is input into an outer function f(x). A good choice for g(x) would be a function inside the composite parts of h(x), and in this case, we can identify g(x) = 3x - 5 as our inner function since it is common in both terms of h(x).
Once we've identified g(x), we can determine f(x) by substituting g(x) into the original equation h(x). This gives us f(g(x)) = g(x)^3 + \frac{1}{g(x)}. Since g(x) is our variable in this context, we rewrite this in terms of x to get the outer function: f(x) = x^3 + \frac{1}{x}.
Therefore, the two functions that form the composite function h(x) = f(g(x)) are f(x) = x^3 + \frac{1}{x} and g(x) = 3x - 5.