8. Consider the set f = {(x, y) E Z xZ:x+3y = 4}. Is this a function from Z to Z? Explain. %3D %3D
8. Consider the set f = {(x, y) E Z xZ:x+3y = 4}. Is this a function from Z to Z? Explain. %3D %3D
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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Question 8 please 12.2

Transcribed Image Text:# Educational Text - Functions
## Exercises for Section 12.1
1. **Exercise 1**
Suppose \( A = \{0, 1, 2, 3, 4\}, B = \{2, 3, 4, 5\} \) and \( f = \{(0,3), (1,3), (2,4), (3,2), (4,2)\} \).
State the domain and range of \( f \). Find \( f(2) \) and \( f(1) \).
2. **Exercise 2**
Suppose \( A = \{a, b, c, d\}, B = \{2, 3, 4, 5, 6\} \) and \( f = \{(a,2), (b,3), (c,4), (d,5)\} \).
State the domain and range of \( f \). Find \( f(b) \) and \( f(d) \).
3. **Exercise 3**
There are four different functions \( f: \{a, b\} \rightarrow \{0, 1\} \).
List them. Diagrams suffice.
4. **Exercise 4**
There are eight different functions \( f: \{a, b, c\} \rightarrow \{0, 1\} \).
List them. Diagrams suffice.
5. **Exercise 5**
Give an example of a relation from \( \{a, b, c, d\} \) to \( \{d, e\} \) that is not a function.
6. **Exercise 6** (Highlighted)
Suppose \( f: \mathbb{Z} \rightarrow \mathbb{Z} \) is defined as \( f = \{(x, 4x + 5) : x \in \mathbb{Z}\} \).
State the domain, codomain, and range of \( f \). Find \( f(10) \).
7. **Exercise 7**
Consider the set \( f = \{(x, y) \in \mathbb{Z} \times \mathbb{Z} : 3x + y = 4\}
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