2. For each of the following functions decide whether it is one-to-one and whether it is onto, and give a brief justification for your answers. (i) m: QxQ→ Q with (a, b) → ab. (ii) ƒ : Z → P(N) with f(z) = {p € N; plz and p prime}. Note that P(N) denotes the power set of N, which is the set of all subsets of N. (iii) F: Z \ {0} → NU {0} with F(2) = f(z)], where f is as given in (ii), and where for a finite set A, |A| denotes the number of elements in the set A. Why did we have to remove 0 from the domain?
2. For each of the following functions decide whether it is one-to-one and whether it is onto, and give a brief justification for your answers. (i) m: QxQ→ Q with (a, b) → ab. (ii) ƒ : Z → P(N) with f(z) = {p € N; plz and p prime}. Note that P(N) denotes the power set of N, which is the set of all subsets of N. (iii) F: Z \ {0} → NU {0} with F(2) = f(z)], where f is as given in (ii), and where for a finite set A, |A| denotes the number of elements in the set A. Why did we have to remove 0 from the domain?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.1: Inverse Functions
Problem 17E
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![2. For each of the following functions decide whether it is one-to-one and whether it is
onto, and give a brief justification for your answers.
(i) m : Q × Q → Q with (a, b) → ab.
=
(ii) f: Z → P(N) with f(z) = {p N; plz and p prime}. Note that P(N) denotes
the power set of N, which is the set of all subsets of N.
(iii) F : Z \ {0} → NU {0} with F(z) = [ƒ(z)], where ƒ is as given in (ii), and where
for a finite set A, A denotes the number of elements in the set A.
Why did we have to remove 0 from the domain?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb7f27c73-756c-4a47-8ea7-79b047cfb8fe%2F25faf2e9-3e28-499d-8a44-0f0b825b3359%2Fd5oqxkh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. For each of the following functions decide whether it is one-to-one and whether it is
onto, and give a brief justification for your answers.
(i) m : Q × Q → Q with (a, b) → ab.
=
(ii) f: Z → P(N) with f(z) = {p N; plz and p prime}. Note that P(N) denotes
the power set of N, which is the set of all subsets of N.
(iii) F : Z \ {0} → NU {0} with F(z) = [ƒ(z)], where ƒ is as given in (ii), and where
for a finite set A, A denotes the number of elements in the set A.
Why did we have to remove 0 from the domain?
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