Final answer:
The question addresses the composition of the two functions f(x) = 1/x and a piecewise g(x) function, involving a discussion about properties of even and odd functions, graphing restrictions, and the concept of inverting functions and negative exponents.
Step-by-step explanation:
The question invites us to analyze the composition of two functions, f(x) = 1/x and a piecewise function g(x), which is defined differently depending on whether x is greater than or less than zero. The composition g ∘ f involves applying f first and then g. The relevance of properties such as even and odd functions and their multiplication rules arises from attempting to understand the nature of function composition. When considering f(x) for values 0 ≤ x ≤ 20, the graph is a portion of a horizontal line between these two values, indicating constant behavior on that interval.
The mention of inverting mathematical functions relates to finding the inverse function, or the process of solving for a variable when its exponent is not one. This kind of manipulation is frequently needed in composition and inversion of functions. Lastly, the reference to negative exponents highlights that they represent the reciprocal of a number, which is pertinent to the given f(x) = 1/x, where x has a negative exponent.