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Unformatted text preview: under f, ༉ a is called the preimage of b. ༉ “f (a)” is also known as the range. ༉ Two functions are equal when they have the same domain, the same codomain and map each element of the domain to the same element of the codomain. Represen$ng Func$ons ༉ Functions may be speciﬁed in diﬀerent ways: 1. An explicit statement of the assignment. ༉ For instance, students and grades example. 2. A formula: ༉ f(x) = x + 1 3. A computer program: ༉ A Java program that when given an integer n, produces the nth Fibonacci Number (covered in the next section and also in Chapter 5). Ques$ons f (a) = ? z The image of d is ? z The domain of f is ? A The codomain of f is ? B b
The preimage of y is ? The preimage(s) of z is (are) ? {a, c, d} A B a
x
b y c
d z Ques$on on Func$ons and Sets ༉ If and S is a subset of A, then A B a
x f ({a, b, c}) is ? {y, z} b y c f ({c, d}) is ? {z} d z Injec$ons Deﬁnition: a function f is said to be one to one if and only if for all a and b in the domain, f (a) = f (b) implies that a = b. ༉ A function is said to be an injection if it is one to one. YES! YES! NO! Surjec$ons Deﬁnition: a function f from A to B is called onto, if and only if for every element b ! Y, there is an element a ! X with f (a) = b. ༉ ...
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This document was uploaded on 02/27/2014 for the course CS 215 at SIU Carbondale.
 Spring '14
 M.Nojoumian
 Computer Science

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