Skip to main content
Ch. 2 - Functions and Graphs
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 8th EditionCh. 2 - Functions and GraphsProblema 7a
Capitolo 3, Problema 7a

Find the domain of each function. g(x) = 3/(x2-2x-15)

Guida verificata passo dopo passo
1
Step 1: Recall that the domain of a function is the set of all possible input values (x-values) for which the function is defined. For rational functions like g(x) = 3/(x^2 - 2x - 15), the function is undefined when the denominator equals zero.
Step 2: Set the denominator equal to zero to find the x-values that make the function undefined. Solve the equation x^2 - 2x - 15 = 0.
Step 3: Factor the quadratic expression x^2 - 2x - 15. Look for two numbers that multiply to -15 and add to -2. These numbers are -5 and 3, so the factorization is (x - 5)(x + 3).
Step 4: Solve the factored equation (x - 5)(x + 3) = 0. Set each factor equal to zero: x - 5 = 0 and x + 3 = 0. Solve for x to find x = 5 and x = -3.
Step 5: Exclude the values x = 5 and x = -3 from the domain, as these make the denominator zero. The domain of g(x) is all real numbers except x = 5 and x = -3, which can be written in interval notation as (-∞, -3) ∪ (-3, 5) ∪ (5, ∞).

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
3m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Domain of a Function

The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. For rational functions, the domain is typically restricted by values that would make the denominator zero, as division by zero is undefined.
Video consigliato:
Percorso guidato
3:51
Domain Restrictions of Composed Functions

Factoring Quadratic Expressions

Factoring quadratic expressions involves rewriting them as a product of their linear factors. This is essential for identifying the values that make the denominator zero. In the case of g(x) = 3/(x^2-2x-15), factoring the quadratic will help determine the critical points that affect the domain.
Video consigliato:
Percorso guidato
06:08
Solving Quadratic Equations by Factoring

Finding Asymptotes

Asymptotes are lines that a graph approaches but never touches. For rational functions, vertical asymptotes occur at the x-values that make the denominator zero. Understanding asymptotes is crucial for determining the domain, as these points indicate where the function is undefined.
Video consigliato:
Percorso guidato
6:24
Introduction to Asymptotes
Pratica correlata
Domanda del libro di testo

Find f(g(x)) and g (f(x)) and determine whether each pair of functions ƒ and g are inverses of each other. f(x) = = -x and g(x) = -x

633
views
Domanda del libro di testo

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (2, −3) and perpendicular to the line whose equation is y = (1/5)x + 6

81
views
Domanda del libro di testo

In Exercises 1–10, determine whether each relation is a function. Give the domain and range for each relation. {(1, 4), (1, 5), (1, 6)}

142
views
Domanda del libro di testo

Find f(g(x)) and g (f(x)) and determine whether each pair of functions ƒ and g are inverses of each other. f(x) = 3/(x-4) and g(x) = (3/x) + 4

680
views
Domanda del libro di testo

Evaluate each function at the given values of the independent variable and simplify. g(x) = 3x^2 - 5x + 2 (a) g(0), (b) g(-2), (c) g(x-1), (d) g(-x)

207
views
Domanda del libro di testo

Use the graph of y = f(x) to graph each function g.

g(x) = f(-x)

899
views