Consider the following function: f: Z → N given by f(x) = (x+4)² +5; where, as usual, Z and N, denote the set of all integers and the set of all natural numbers, respectively. You are given that the function f is not an injection. In order to show that f is not an injection, state two distinct elements of the domain of f, denoted by ₁, 2, such that f(x₁) = f(x₂). ● State ₁: • State #₂: You are given that the function f is not a surjection. In order to show that f is not a surjection, state an element of the codomain of f, denoted by y, that is not in the image of f. • State y:
Consider the following function: f: Z → N given by f(x) = (x+4)² +5; where, as usual, Z and N, denote the set of all integers and the set of all natural numbers, respectively. You are given that the function f is not an injection. In order to show that f is not an injection, state two distinct elements of the domain of f, denoted by ₁, 2, such that f(x₁) = f(x₂). ● State ₁: • State #₂: You are given that the function f is not a surjection. In order to show that f is not a surjection, state an element of the codomain of f, denoted by y, that is not in the image of f. • State y:
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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Transcribed Image Text:Consider the following function:
f: Z→ N given by f(x) = (x + 4)² + 5;
where, as usual, Z and N, denote the set of all integers and the set of all natural numbers, respectively.
You are given that the function f is not an injection.
In order to show that f is not an injection, state two distinct elements of the domain of f, denoted by ₁, 2, such that f(x₁) = f(x₂).
● State ₁:
• State x₂:
You are given that the function f is not a surjection.
In order to show that f is not a surjection, state an element of the codomain of f, denoted by y, that is not in the image of f.
• State y:
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