Final answer:
A composite function f(g(x)) is formed by combining a constant function f(x) with another function g(x). If g(x) involves a horizontal translation, f(g(x)) will reflect this translation while maintaining the same y-value.
Step-by-step explanation:
The student is asking about composite functions and function transformation. The given function f(x) is a constant function represented by a horizontal line at y = 20 throughout the interval 0 ≤ x ≤ 20. A composite function in the form of f(g(x)) can be created by inserting another function g(x) into f(x).
For example, if we have a function g(x) that translates the original function f(x) in the x-direction by a distance d, then f(g(x)) would use g(x) as the input for f. If g(x) = x - d, then the composite function f(g(x)) = f(x - d) is the horizontal line y = 20, shifted to the right by distance d. If g(x) = x + d, then f(g(x)) = f(x + d) is the horizontal line y = 20, shifted to the left by distance d.