Question 3. (a) Define precisely what it means for a function f : A → B to be injective. (b) For each of the following functions, determine whether or not the function is injective justifying your answers. (i) t : Z → Z, t(n) = n – 2020 (ii) u : P(N) → P(N), u(S) = S{1,2,3} (iii) s:C → C, s(z)= z² (iv) p : N x N → N, p(n,m) = n+m

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 51E
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Question 3.
(a) Define precisely what it means for a function f : A → B to be injective.
(b) For each of the following functions, determine whether or not the function is
injective justifying your answers.
(i) t : Z → Z, t(n)
(ii) u : P(N) → P(N), u(S) = SU{1,2,3}
(iii) s:C → C, s(z) = z²
(iv) p : N × N → N, p(n,m) = n+m
= n – 2020
Transcribed Image Text:Question 3. (a) Define precisely what it means for a function f : A → B to be injective. (b) For each of the following functions, determine whether or not the function is injective justifying your answers. (i) t : Z → Z, t(n) (ii) u : P(N) → P(N), u(S) = SU{1,2,3} (iii) s:C → C, s(z) = z² (iv) p : N × N → N, p(n,m) = n+m = n – 2020
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