In applications, the symbols used for the independent and dependent variables are often ba...

In applications, the symbols used for the independent and dependent variables are often based on common usage. So, rather than using y = f(x) to represent a function, an applied problem might use C = C(q) to represent the cost C of manufacturing q units of a good since, in economics, q is used for output. Because of this, the inverse notation f–1 used in a pure mathematics problem is not used when finding inverses of applied problems. Rather, the inverse of a function such as C = C(q) will be q = q(C). So C = C(q) is a function that represents the cost C as a function of the output q, while q = q(C) is a function that represents the output q as a function of the cost C. Problems illustrate this idea.

Given

find f–1(x). If c ≠ 0, under what conditions on a, b, c, and d

is f = f–1?