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Unformatted text preview: 1 CMSC 250 Functions 2 CMSC 250 Function terminology ● A function maps elements of one set (called the domain) to another set (called the codomain) . ● Domain : the set which contains the values to which the function is applied ● Codomain : the set which contains the possible values (results) of the function ● Image : the set of actual values produced when applying the function to the values of the domain Formally the image of f is { y ∈ Y  ( 5 x ∈ X )[ f(x) = y ]} 3 CMSC 250 More function terminology ● f : X → Y – f is the function name – X is the domain – Y is the codomain – f(x) = y means f maps x to y 4 CMSC 250 Formal definitions ● Image of function (in class) ● Inverse image of a point (in class) ● f = g if – f and g have the same domain – f and g have the same codomain – For all x (in domain), f ( x )= g ( x ) 5 CMSC 250 Types of functions ● F : X → Y is onetoone (or injective ) if ( 2200 x 1 , x 2 ∈ X )[ F ( x 1 ) = F ( x 2 ) → x 1 = x 2 ], or alternatively ( 2200 x 1 , x 2 ∈ X )[ x 1 ≠ x 2 → F ( x 1 ) ≠ F ( x 2 )] ● F : X → Y is onto (or surjective ) if ( 2200 y ∈ Y )( 5 x ∈ X )[ F ( x ) = y ] ● F : X → Y is not onetoone if ( 5 x 1 , x 2 ∈ X )[( x 1 ≠ x 2 ) ^ ( F ( x 1 ) = F ( x 2 ))] ● F : X → Y is not onto...
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This note was uploaded on 12/04/2011 for the course CMSC 250 taught by Professor Staff during the Spring '08 term at Maryland.
 Spring '08
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