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1. Let f: ZZ be defined by f(x) = -x for all x € Z. Is f injective?

1. Let f: ZZ be defined by f(x) = -x for all x € Z. Is f injective?

Advanced Engineering Mathematics
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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1. Let f: Z→ Z be defined by f(x) = -x for all x E Z. Is f injective? 2. Let g: NN be defined by f(n) = n + 1 for all n E N. Is f surjective? 3. Give an example of a bijective function between the sets S = {a, b, c, d) and T = {x, y, z) or explain why one does not exist. [If providing a function, use an arrow diagram, two-line notation, or a graph.]
Transcribed Image Text:1. Let f: Z→ Z be defined by f(x) = -x for all x E Z. Is f injective? 2. Let g: NN be defined by f(n) = n + 1 for all n E N. Is f surjective? 3. Give an example of a bijective function between the sets S = {a, b, c, d) and T = {x, y, z) or explain why one does not exist. [If providing a function, use an arrow diagram, two-line notation, or a graph.]
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