Final answer:
The functions f(x) and g(x) are found by realizing that g(x) should be x + 7 and then finding f(x) to be a cubic polynomial that results in the given h(x) when composed with g(x). Therefore, f(x) is x^3 - 3x^2 + 4x - 1 and g(x) is x + 7.
Step-by-step explanation:
The student is asking for the determination of functions f(x) and g(x) such that the composition of these two functions (f•g)(x) results in a given function h(x). In this case, h(x) can be expressed as a cubic polynomial in terms of x + 7. Each term of h(x) includes this expression to a power. This suggests that g(x) could be the function x + 7, and f(u) would then be a function of u that manipulates this expression in such a way to achieve the desired result when composed with g(x).
To find f(u) based on the given h(x), we can substitute u = g(x) = x + 7 into h(x) to get a new expression representing f(u). Taking h(x) fully in terms of u, we can find f(u) = u^3 - 3u^2 + 4u - 1. Therefore, we have f(x) = x^3 - 3x^2 + 4x - 1 and g(x) = x + 7. By simply substituting x + 7 back into u in f(u), we get the original h(x) as required.