1. • For each of the following functions, determine whether the function is: Injective (one-to-one). ● Surjective (onto). Bijective. Justify your answers. 1.1 ƒ:Z+ → Z+ such that f(x) = 5 + x. 1.2 f:Z → Z such that f(x) = 5 + x. 1.3 f: R → Z such that f(x) = [4x] (i.e., ceiling of 4x). 1.4 f: R→ R such that f(x) = |x + 1|. 1.5 ƒ:Z × Z → Z such that f(x, y) = xy.
1. • For each of the following functions, determine whether the function is: Injective (one-to-one). ● Surjective (onto). Bijective. Justify your answers. 1.1 ƒ:Z+ → Z+ such that f(x) = 5 + x. 1.2 f:Z → Z such that f(x) = 5 + x. 1.3 f: R → Z such that f(x) = [4x] (i.e., ceiling of 4x). 1.4 f: R→ R such that f(x) = |x + 1|. 1.5 ƒ:Z × Z → Z such that f(x, y) = xy.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.4: Definition Of Function
Problem 58E
Related questions
Question
![1.
•
For each of the following functions, determine whether the function is:
Injective (one-to-one).
●
Surjective (onto).
Bijective.
Justify your answers.
1.1 ƒ:Z+ → Z+ such that f(x) = 5 + x.
1.2 f:Z → Z such that f(x) = 5 + x.
1.3 f: R → Z such that f(x) = [4x] (i.e., ceiling of 4x).
1.4 f: R→ R such that f(x) = |x + 1|.
1.5 ƒ:Z × Z → Z such that f(x, y) = xy.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7e548bee-1bde-48b8-a7d0-72068d2a0767%2F07f03b30-9f7e-4417-a816-5b3c94f43f1b%2Fhnd1bls_processed.png&w=3840&q=75)
Transcribed Image Text:1.
•
For each of the following functions, determine whether the function is:
Injective (one-to-one).
●
Surjective (onto).
Bijective.
Justify your answers.
1.1 ƒ:Z+ → Z+ such that f(x) = 5 + x.
1.2 f:Z → Z such that f(x) = 5 + x.
1.3 f: R → Z such that f(x) = [4x] (i.e., ceiling of 4x).
1.4 f: R→ R such that f(x) = |x + 1|.
1.5 ƒ:Z × Z → Z such that f(x, y) = xy.
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