For each of the following functions, determine whether the function is: • Injective (one-to-one). • Surjective (onto). Bijective. Justify your answers. a. f:Z→ Z such that f(x) = 2x +1. b. f:Z→ Z such that f(x) = [x/2] (1.e., floor of x/2).

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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Part A and B only please.

Part II: Functions
3.
For each of the following functions, determine whether the function is:
• Injective (one-to-one).
• Surjective (onto).
Bijective.
Justify your answers.
a. f:Z→ Z such that f(x) = 2x + 1.
b. f:Z- Z such that f(x) = [x/2] (1.e., floor of x/2).
c. f:Z* - Z+ such that f(x) = |x| + 1.
d. f:Z x Z- Z such that f(x, y) = x + y.
Transcribed Image Text:Part II: Functions 3. For each of the following functions, determine whether the function is: • Injective (one-to-one). • Surjective (onto). Bijective. Justify your answers. a. f:Z→ Z such that f(x) = 2x + 1. b. f:Z- Z such that f(x) = [x/2] (1.e., floor of x/2). c. f:Z* - Z+ such that f(x) = |x| + 1. d. f:Z x Z- Z such that f(x, y) = x + y.
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