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. 

The period T (in seconds) of a simple pendulum as a function of its length l (in feet) is given by

(a) Express the length l as a function of the period T.

(b) How long is a pendulum whose period is 3 seconds?

Transcribed Image Text:

T(1) 2T 1 32.2