This preview shows page 1. Sign up to view the full content.
Unformatted text preview: we should note that this definition of onetoone is not
really the mathematically correct definition of onetoone. It is identical to the mathematically
correct definition it just doesn’t use all the notation from the formal definition.
Now, let’s see an example of a function that isn’t onetoone. The function f ( x ) = x 2 is not
onetoone because both f ( 2 ) = 4 and f ( 2 ) = 4 . In other words there are two different
values of x that produce the same value of y. Note that we can turn f ( x ) = x 2 into a onetoone
function if we restrict ourselves to 0 £ x < ¥ . This can sometimes be done with functions.
Showing that a function is onetoone is often a tedious and often difficult. For the most part we
are going to assume that the functions that we’re going to be dealing with in this section are onetoone. We did need to talk about onetoone functions however since only onetoone functions
can be inverse functions.
Now, let’s formally define just what inverse functions are.
Inverse Functions
Given two onetoone functions f ( x ) and g ( x ) if AND
( f o g )( x) = x
( g o f ) ( x) = x
t...
View
Full
Document
This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.
 Spring '12
 MrVinh

Click to edit the document details