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Unformatted text preview: we should note that this definition of one-to-one is not
really the mathematically correct definition of one-to-one. 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 one-to-one. The function f ( x ) = x 2 is not
one-to-one 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 one-to-one
function if we restrict ourselves to 0 £ x < ¥ . This can sometimes be done with functions.
Showing that a function is one-to-one 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 oneto-one. We did need to talk about one-to-one functions however since only one-to-one functions
can be inverse functions.
Now, let’s formally define just what inverse functions are.
Given two one-to-one functions f ( x ) and g ( x ) if AND
( f o g )( x) = x
( g o f ) ( x) = x
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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