Domanda del libro di testo
Determine whether each relation is a funciton, Give the domain and range for each relation. (1, 10), (2, 500), (13, π)
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Ch. 2 - Functions and Graphs
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- 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
Capitolo 3, Problema 3
Find the domain of each function. g(x) = 3/(x-4)
Guida verificata passo dopo passo1
Identify the function given: \(g(x) = \frac{3}{x-4}\). Since this is a rational function, the domain includes all real numbers except where the denominator is zero.
Set the denominator equal to zero to find values that are not allowed: \(x - 4 = 0\).
Solve the equation for \(x\): \(x = 4\). This value makes the denominator zero, which is undefined in mathematics.
Therefore, the domain of \(g(x)\) is all real numbers except \(x = 4\).
Express the domain in interval notation: \((-\infty, 4) \cup (4, \infty)\).
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Domain of a Function
The domain of a function is the set of all possible input values (x-values) for which the function is defined. It excludes any values that cause undefined expressions, such as division by zero or taking the square root of a negative number in real numbers.
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3:51
Domain Restrictions of Composed Functions
Restrictions from Denominators
When a function includes a denominator, the values that make the denominator zero are excluded from the domain because division by zero is undefined. To find these restrictions, set the denominator equal to zero and solve for x.
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02:58Rationalizing Denominators
Rational Functions
A rational function is a ratio of two polynomials. Its domain includes all real numbers except those that make the denominator zero. Understanding rational functions helps in identifying domain restrictions and behavior near excluded values.
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6:04Intro to Rational Functions
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