Lec09_Functions - TDS1191 Discrete Structures Lecture 09...

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Discrete Structures 1 TDS1191 Discrete Structures Lecture 09 Functions Multimedia University Trimester 2 Session 2011/2012 [Lecture 9][Function]
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Discrete Structures 2 [Introduction] From Relations to Functions Sum and Product of Functions Image of Subset Properties of Functions Inverse Functions Composition of Functions Graph of a Function Floor and Ceiling Functions [Lecture 9][Function]
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Discrete Structures 3 Definition: A function f from a nonempty set A to a nonempty set B is an assignment of exactly one element of B to each element of A. We write the function as f : A B. Functions are also called mappings or transformations. - b = f(a) is called the image of a under f , and a is called the preimage of b. - A is the domain of f and B is the co-domain - f(A) = { f(a) | a A } is called the range of f a A b= ƒ (a) B f [Lecture 9][Function]
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Discrete Structures 4 From relations to functions A relation f from A to B is a function if: Every element of A is related to some element of B An element of A cannot be related to more than one element of B i.e. 2200 a A 5 b B (((a,b) f) ( 2200 b’ B ((b’≠b) ((a, b’) f)))) [Lecture 9][Function] 1 2 3 4 a b c A function Not a function because of A B 1 2 3 4 a b c A B
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Discrete Structures 5 Functions 1) Dig into the definition of the following function and give all elements of f as a relation. f : {1,2,3} x {3,4} N f(a,b) = a + b 2) Can you think of a relation being NOT a function. [Lecture 9][Function]
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Discrete Structures 6 Let f be f : R R f(x) = x 2 Give domain, co-domain, and the images of - 6 and 6. Let f be f : Country City f(a) = capital city of a Give domain, co-domain, and the image of Malaysia and Brunei. Let f be as in the diagram to the right Give domain, co-domain and the range of f. 1 2 3 4 a b c [Lecture 9][Function] Functions … cont’d
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Discrete Structures 7 Look at the relations below represented by diagrams. Determine whether the relations are functions, and explain why.
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Lec09_Functions - TDS1191 Discrete Structures Lecture 09...

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