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Ch. R - Review of Basic Concepts
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Lial 13th EditionCh. R - Review of Basic Concepts문제 19a
1장, 문제 19a

Find the domain of each rational expression. x3 - 1 / x - 1

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1
Identify the rational expression given: \(\frac{x^3 - 1}{x - 1}\).
Recall that the domain of a rational expression excludes values that make the denominator zero, because division by zero is undefined.
Set the denominator equal to zero and solve for \(x\): \(x - 1 = 0\).
Solve the equation to find the value(s) to exclude from the domain: \(x = 1\).
Conclude that the domain is all real numbers except \(x = 1\), which can be written in interval notation as \((-\infty, 1) \cup (1, \infty)\).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Rational Expressions

A rational expression is a fraction where both the numerator and denominator are polynomials. Understanding rational expressions involves knowing how to simplify, factor, and analyze these fractions, especially focusing on restrictions caused by the denominator.
추천 영상:
02:58
Rationalizing Denominators

Domain of a Function

The domain of a function is the set of all input values (x-values) for which the function is defined. For rational expressions, the domain excludes values that make the denominator zero, as division by zero is undefined.
추천 영상:
3:51
Domain Restrictions of Composed Functions

Factoring Polynomials

Factoring polynomials involves rewriting a polynomial as a product of simpler polynomials. This skill helps identify values that make the denominator zero by factoring and setting each factor equal to zero to find restrictions on the domain.
추천 영상:
07:30
Introduction to Factoring Polynomials
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