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Consider the function f : {4, 6, 7, 8, 9} → {1, 2, 4, 5, 6, 9} given by the table below: 4 6 7 8 9 f(x) 1 2 5 96 X a. Is f injective? Why or why not? OYes, because every element in the codomain is the image of at most one element of the domain. No, because at least one element in the codomain is the image of two or more elements of the domain. Yes, because every element in the codomain is the image of at least one element of the domain. O No, because at least one element in the codomain is not the image to an element of the domain. b. Is f surjective? Why or why not? Yes, because every element in the codomain is the image of at most one element of the domain. O No, because at least one element in the codomain is the image of two or more elements of the domain. Yes, because every element in the codomain is the image of at least one element of the domain. O No, because at least one element in the codomain is not the image to an element of the domain.

Consider the function f : {4, 6, 7, 8, 9} → {1, 2, 4, 5, 6, 9} given by the table below: 4 6 7 8 9 f(x) 1 2 5 96 X a. Is f injective? Why or why not? OYes, because every element in the codomain is the image of at most one element of the domain. No, because at least one element in the codomain is the image of two or more elements of the domain. Yes, because every element in the codomain is the image of at least one element of the domain. O No, because at least one element in the codomain is not the image to an element of the domain. b. Is f surjective? Why or why not? Yes, because every element in the codomain is the image of at most one element of the domain. O No, because at least one element in the codomain is the image of two or more elements of the domain. Yes, because every element in the codomain is the image of at least one element of the domain. O No, because at least one element in the codomain is not the image to an element of the domain.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.2: Mappings
Problem 11E: For the given f:ZZ, decide whether f is onto and whether it is one-to-one. Prove that your decisions...
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Consider the function ƒ : {4, 6, 7, 8, 9} → {1, 2, 4, 5, 6, 9} given by the table below: 4 6 7 8 9 f(x) 1 2 596 X a. Is f injective? Why or why not? Yes, because every element in the codomain is the image of at most one element of the domain. O No, because at least one element in the codomain is the image of two or more elements of the domain. Yes, because every element in the codomain is the image of at least one element of the domain. No, because at least one element in the codomain is not the image to an element of the domain. b. Is f surjective? Why or why not? Yes, because every element in the codomain is the image of at most one element of the domain. No, because at least one element in the codomain is the image of two or more elements of the domain. Yes, because every element in the codomain is the image of at least one element of the domain. No, because at least one element in the codomain is not the image to an element of the domain. 0000
Transcribed Image Text:Consider the function ƒ : {4, 6, 7, 8, 9} → {1, 2, 4, 5, 6, 9} given by the table below: 4 6 7 8 9 f(x) 1 2 596 X a. Is f injective? Why or why not? Yes, because every element in the codomain is the image of at most one element of the domain. O No, because at least one element in the codomain is the image of two or more elements of the domain. Yes, because every element in the codomain is the image of at least one element of the domain. No, because at least one element in the codomain is not the image to an element of the domain. b. Is f surjective? Why or why not? Yes, because every element in the codomain is the image of at most one element of the domain. No, because at least one element in the codomain is the image of two or more elements of the domain. Yes, because every element in the codomain is the image of at least one element of the domain. No, because at least one element in the codomain is not the image to an element of the domain. 0000
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