For each one, classify it as Injective but not surjective, Surjective but not injective, Neither injective nor surjective, or Bijective. If a function does have a property you do not have to explain why; but if a function fails to have a property, you should explain why in as specific of terms as possible. f:Z→Z given by f(a)=2a g:N→N given by g(a)=a2−1 The mapping h from the set of all lists of integers (such as [7,3,-2,10]) to Z that takes the list and returns the sum of the elements in the list. For example h([7,3,−2,10])=18
For each one, classify it as Injective but not surjective, Surjective but not injective, Neither injective nor surjective, or Bijective. If a function does have a property you do not have to explain why; but if a function fails to have a property, you should explain why in as specific of terms as possible. f:Z→Z given by f(a)=2a g:N→N given by g(a)=a2−1 The mapping h from the set of all lists of integers (such as [7,3,-2,10]) to Z that takes the list and returns the sum of the elements in the list. For example h([7,3,−2,10])=18
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
For each one, classify it as
- Injective but not surjective,
- Surjective but not injective,
- Neither injective nor surjective, or
- Bijective.
If a function does have a property you do not have to explain why; but if a function fails to have a property, you should explain why in as specific of terms as possible.
- f:Z→Z given by f(a)=2a
- g:N→N given by g(a)=a2−1
- The mapping h from the set of all lists of integers (such as [7,3,-2,10]) to Z that takes the list and returns the sum of the elements in the list. For example h([7,3,−2,10])=18
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