10-6 Class notes

In practical expressions and formulas, the variable isolated on one side of the equal sign is usually the output or range variable.  The other variable, mixed with operations and quantities, is usually the input or domain variable.

F(A) = Cost = 30 + 80A, where A is a domain value measured in acres.  The range is measured in dollars.

G(C) = Area = C - 30, obtained by isolating A and solving for A.  C is now a domain value measured                             80
in dollars, and the range is the output measured in acres.

F and G are inverse functions.  The domain and range traded places.

F(A) when A = 3/8 is F(3/8) = 30 + 80(3/8) = 30 + 30 = 60

G(F(A) uses the original function inside the inverse function.
Substitute 60 for F(A).  Evaluate G(60).

G(60) = 60 - 30  = 30/80 = 3/8.    Note that when 3/8 is the input to function F, 60 is the output.
                 80
                                                     When 60 is the input in the inverse function G, 3/8 is the output.