This means that each point in the range has a unique pre-image (element of the domain).
for any y in B.
In this section we introduce the inverse function, which is the mirror image of f about the line y=x. Hence, properties of are also mirror reflections of those properties of f. It's easy to graph , for example, once we have the graph of f, and properties of continuity and differentiability are also easy to deduce. Even asymptotes are reflected! It's even easy to compute slopes at a point on the inverse function if we know the derivative of the function f.
One can think of f and as ways of passing between two sets (the domain and range of f, which are the range and domain of ). A secret code is an example of a function and its inverse: if I give you a secret message, it's tranformed from an ordinary expression (the domain) by a function and passed into a strange form (in the range). The secret agent on the other end needs a method (the inverse function) that turns strange forms into ordinary expressions.
Problems:
Problems, pp. 414-416, #2-10, 12, 14, 16, 22, 23, 34, 38,
In class: #7-10, 13, 15, 24, 33, 36