Consider the function f= {(n,n² –1) such that n<5,n€N}, written in set-builder notation, which defines a set containing a list of ordered pairs. Write the inverse of f as a set in list form containing ordered pairs.
Consider the function f= {(n,n² –1) such that n<5,n€N}, written in set-builder notation, which defines a set containing a list of ordered pairs. Write the inverse of f as a set in list form containing ordered pairs.
Computer Networking: A Top-Down Approach (7th Edition)
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Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
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![**Title: Understanding Inverse Functions through Set-Builder Notation**
**Introduction:**
Consider the function \( f = \{(n, n^2 - 1) \} \) such that \( n < 5 \) and \( n \in \mathbb{N} \), written in set-builder notation, which defines a set containing a list of ordered pairs.
---
**Objective:**
Write the inverse of \( f \) as a set in list form containing ordered pairs.
**Options:**
1. \( f^{-1} = \{(0,1), (3,2), (8,3), (15,4)\} \)
2. \( f^{-1} = \{(0, -1), (1,0), (2,3), (3,8), (4,15)\} \)
3. \( f^{-1} = \{(1,0), (2,3), (3,8), (4,15)\} \)
4. \( f^{-1} = \{(-1,0), (0,1), (3,2), (8,3), (15,4)\} \)
5. \( f^{-1} = \{(3,2), (8,3), (15,4)\} \)
---
**Explanation:**
To find the correct inverse of the function \( f \), we begin by identifying the original set of ordered pairs from the function \( f \). The function \( f \) is defined as:
\[ f = \{(n, n^2 - 1) \mid n < 5, n \in \mathbb{N}\} \]
Here \( \mathbb{N} \) represents the set of natural numbers.
As per the definition, we need to identify the elements \( (n, n^2 - 1) \) for \( n = 1, 2, 3, 4 \):
1. For \( n = 1 \): \( (1, 1^2 - 1) = (1, 0) \)
2. For \( n = 2 \): \( (2, 2^2 - 1) = (2, 3) \)
3. For \( n = 3 \): \( (3, 3^2 - 1) = (3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F92664a72-5e56-42ce-9287-433ae5912718%2Fada447f8-b85a-48c7-a4e6-1809fe4e3932%2Fsqi2g84_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Inverse Functions through Set-Builder Notation**
**Introduction:**
Consider the function \( f = \{(n, n^2 - 1) \} \) such that \( n < 5 \) and \( n \in \mathbb{N} \), written in set-builder notation, which defines a set containing a list of ordered pairs.
---
**Objective:**
Write the inverse of \( f \) as a set in list form containing ordered pairs.
**Options:**
1. \( f^{-1} = \{(0,1), (3,2), (8,3), (15,4)\} \)
2. \( f^{-1} = \{(0, -1), (1,0), (2,3), (3,8), (4,15)\} \)
3. \( f^{-1} = \{(1,0), (2,3), (3,8), (4,15)\} \)
4. \( f^{-1} = \{(-1,0), (0,1), (3,2), (8,3), (15,4)\} \)
5. \( f^{-1} = \{(3,2), (8,3), (15,4)\} \)
---
**Explanation:**
To find the correct inverse of the function \( f \), we begin by identifying the original set of ordered pairs from the function \( f \). The function \( f \) is defined as:
\[ f = \{(n, n^2 - 1) \mid n < 5, n \in \mathbb{N}\} \]
Here \( \mathbb{N} \) represents the set of natural numbers.
As per the definition, we need to identify the elements \( (n, n^2 - 1) \) for \( n = 1, 2, 3, 4 \):
1. For \( n = 1 \): \( (1, 1^2 - 1) = (1, 0) \)
2. For \( n = 2 \): \( (2, 2^2 - 1) = (2, 3) \)
3. For \( n = 3 \): \( (3, 3^2 - 1) = (3
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