# 20 - LECTURE 20: FUNCTIONS (9.1-9.2) Success is more a...

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LECTURE 20: FUNCTIONS ( § 9.1-9.2) Success is more a function of consistent common sense than it is of genius. An Wang 1. What are functions? Let A and B be two non-empty sets. A function f from A to B , written f : A B , is a relation (i.e. a subset of A × B ) where each element of A occurs as the ﬁrst coordinate of exactly one ordered pair. We think of that ordered pair ( a,b ) as telling us where a is mapped to: b = f ( a ). Example 1. Let f : R R be given by the rule f ( x ) = x 2 . We can also think of f as the set of ordered pairs f = { ( x,y ) R × R : y = x 2 } . Notice that each element of A = R occurs exactly once as a ﬁrst coordinate. The set A is called the domain . The set B is called the codomain . The set of elements inside B which do occur as second coordinates is called the range . We usually write dom( f ) for the domain, and ran( f ) for the range. Example 2. Let f : R R be given by the rule f ( x ) = x 2 . The domain is R , the codomain is R , and
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## This note was uploaded on 03/08/2011 for the course MATH 334 taught by Professor Smith during the Spring '11 term at Vanderbilt.

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