Domanda del libro di testo
Express the given function h as a composition of two functions ƒ and g so that h(x) = (fog) (x). h(x) = ∛(x² – 9)
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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 77
Find the domain of each function. g(x) = 4/(x - 7)
Guida verificata passo dopo passo1
Identify the function given: \(g(x) = \frac{4}{x - 7}\).
Recall that the domain of a function includes all real numbers except those that make the denominator zero, because division by zero is undefined.
Set the denominator equal to zero to find values to exclude: \(x - 7 = 0\).
Solve the equation for \(x\): \(x = 7\).
Conclude that the domain of \(g(x)\) is all real numbers except \(x = 7\), which can be written in interval notation as \((-\infty, 7) \cup (7, \infty)\).
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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 the real number system.
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3:51
Domain Restrictions of Composed Functions
Restrictions from Denominators
When a function includes a fraction, the denominator cannot be zero because division by zero is undefined. To find the domain, identify values of x that make the denominator zero and exclude them from the domain.
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02:58Rationalizing Denominators
Solving Equations to Find Domain Restrictions
To determine domain restrictions, set the denominator equal to zero and solve for x. The solutions are the values that must be excluded from the domain. For g(x) = 4/(x - 7), solve x - 7 = 0 to find the restricted value.
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3:51Domain Restrictions of Composed Functions
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