Textbook Question
In Exercises 1–6, find all numbers that must be excluded from the domain of each rational expression. (x−1)/(x2+11x+10)
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Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 1, Problem 5
Let A = {a, b, c}, B = {a, c, d, e}, and C = {a, d, f, g}. Find the indicated set A ∪ B.
Verified step by step guidance1
Identify the elements in set A: \( A = \{a, b, c\} \).
Identify the elements in set B: \( B = \{a, c, d, e\} \).
The union of two sets, \( A \cup B \), includes all elements that are in either set A or set B or in both.
List all unique elements from both sets A and B.
Combine the elements to form the union set \( A \cup B \).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Set Union
Set union is a fundamental operation in set theory that combines all unique elements from two or more sets. The union of sets A and B, denoted as A ∪ B, includes every element that is in A, in B, or in both. For example, if A = {1, 2} and B = {2, 3}, then A ∪ B = {1, 2, 3}.
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Element Uniqueness
In set theory, each element in a set is unique, meaning that duplicates are not counted. When performing operations like union, any repeated elements from the involved sets are only included once in the resulting set. For instance, if A = {a, b} and B = {b, c}, then A ∪ B = {a, b, c}.
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Set Notation
Set notation is a way to describe sets and their operations using specific symbols and terminology. Common symbols include curly braces for sets, the union symbol (∪) for combining sets, and the empty set symbol (∅) for a set with no elements. Understanding this notation is essential for accurately interpreting and performing set operations.
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Related Practice
Textbook Question
Evaluate each exponential expression in Exercises 1–22. −26
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Textbook Question
In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). x^2+3x, for x=8
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Textbook Question
Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √−25
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Textbook Question
In Exercises 7–14, simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. (3x−9)/(x2−6x+9)
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Textbook Question
Factor out the greatest common factor.
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