Section 7.4 Inverse Functions

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Presentation transcript:

Section 7.4 Inverse Functions

Defns: Relation-set of ordered pairs Function- is a relation in which every x has exactly one y Vertical line test Inverse relation- formed by swapping the x and y coordinates. It may or may not be a function.

Finding inverse relation:

Exs:

The function f is a set of ordered pairs, (x,y), then the changes produced by f can be “undone” by reversing components of all the ordered pairs. The resulting relation (y,x), may or may not be a function. Inverse functions have a special “undoing” relationship.

Example

Ex:

Find the inverses:

Horizontal Line Test b and c ‘s inverses are not functions because they don’t pass the horizontal line test.

There is a relationship between the graph of a function, f, and its inverse f -1. Because inverse functions have ordered pairs with the coordinates interchanged, if the point (a,b) is on the graph of f then the point (b,a) is on the graph of f -1. The points (a,b) and (b,a) are symmetric with respect to the line y=x. Thus graph of f -1 is a reflection of the graph of f about the line y=x.

A function and it’s inverse graphed on the same axis.

(a) (b) (c) (d)

(a) (b) (c) (d)