slides09 - 1 CMSC 250 Functions 2 CMSC 250 Function...

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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 co-domain 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 one-to-one (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 one-to-one 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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slides09 - 1 CMSC 250 Functions 2 CMSC 250 Function...

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