Consider the following function: f: Z → N given by f(x) = (x+4)² + 8; 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 x1, x2, 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: I
Consider the following function: f: Z → N given by f(x) = (x+4)² + 8; 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 x1, x2, 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: I
Chapter3: Functions
Section3.7: Inverse Functions
Problem 6SE: Show that the function fx)=ax is its own inverse for all real numbers a.
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Transcribed Image Text:Consider the following function:
f : Z → N given by ƒ(x) = (x + 4)² + 8;
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 x₁, x2, such that ƒ(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 ƒ, denoted by y
that is not in the image of f.
I
• State y:
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