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. 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 number q of units manufactured, and q = q(C) is a function that represents the number q as a function of the cost C. 

One model for the ideal body weight W for men (in kilograms) as a function of height h (in inches) is given by the function W(h) = 50 + 2.3( h − 60)
(a) What is the ideal weight of a 6-foot man?
(b) Express the height h as a function of weight W.
(c) Verify that h = h(W) is the inverse of W = W(h) by showing that h(W(h)) = h and W( h(W)) = W.
(d) What is the height of a man who is at his ideal weight of 80 kilograms?