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 17a
Capitolo 3, Problema 17a

Find the domain of each function. f(x) = √(x - 3)

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.
Step 2: For the square root function √(x - 3), the expression inside the square root (x - 3) must be greater than or equal to 0 because the square root of a negative number is not defined in the set of real numbers.
Step 3: Set up the inequality x - 3 ≥ 0 to determine the values of x that make the function valid.
Step 4: Solve the inequality x - 3 ≥ 0 by adding 3 to both sides, resulting in x ≥ 3.
Step 5: Conclude that the domain of the function is all x-values such that x ≥ 3. In interval notation, this is written as [3, ∞).

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:
2m

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. Understanding the domain is crucial because it determines the values that can be substituted into the function without resulting in undefined expressions, such as division by zero or taking the square root of a negative number.
Video consigliato:
3:51
Domain Restrictions of Composed Functions

Square Root Function

A square root function, denoted as f(x) = √(x), is defined only for non-negative values of x. This means that the expression inside the square root must be greater than or equal to zero. For the function f(x) = √(x - 3), this condition leads to the requirement that x - 3 must be non-negative, which directly influences the domain.
Video consigliato:
02:20
Imaginary Roots with the Square Root Property

Inequalities

Inequalities are mathematical expressions that show the relationship between two values, indicating whether one is less than, greater than, or equal to the other. In finding the domain of the function f(x) = √(x - 3), we set up the inequality x - 3 ≥ 0, which helps us determine the minimum value of x that keeps the function defined, thus allowing us to find the domain.
Video consigliato:
06:07
Linear Inequalities
Pratica correlata
Domanda del libro di testo

In Exercises 11–26, determine whether each equation defines y as a function of x. 4x = y²

95
views
Domanda del libro di testo

In Exercises 11–26, determine whether each equation defines y as a function of x. x = y²

82
views
Domanda del libro di testo

Use the graph to determine (a) the function's domain, (b) the function's range, (c) the x-intercepts, if any, (d) the y-intercept, if there is one, (e) intervals on which the function is increasing, decreasing or constant, (f) the missing function values, indicated by question marks, below each graph.

440
views
Domanda del libro di testo

Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (-1/4, -1/7) and (3/4, 6/7)

878
views
Domanda del libro di testo

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

g(x) = f(x) - 1

925
views
Domanda del libro di testo

Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (7/3, 1/5) and (1/3, 6/5)

898
views