Domanda del libro di testo
Use intercepts to graph each equation. 6x-3y+15=0
1008
views
Ch. 2 - Functions and Graphs
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
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 71
Find a. (fog) (x) b. the domain of f o g.
f(x) = √x, g(x) = x − 2
Guida verificata passo dopo passo1
Step 1: Understand the composition of functions. The notation (fog)(x) represents the composition of f and g, which means f(g(x)). To find this, substitute g(x) into f(x).
Step 2: Substitute g(x) = x − 2 into f(x) = √x. This gives f(g(x)) = √(x − 2).
Step 3: Analyze the domain of the composition f(g(x)). Since f(x) = √x involves a square root, the expression inside the square root must be non-negative. Therefore, x − 2 ≥ 0.
Step 4: Solve the inequality x − 2 ≥ 0 to find the domain. Add 2 to both sides to get x ≥ 2.
Step 5: Conclude that the domain of f o g is all x-values such that x ≥ 2. In interval notation, this is [2, ∞).
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:
2mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Function Composition
Function composition involves combining two functions, where the output of one function becomes the input of another. In this case, (f o g)(x) means applying g first and then applying f to the result of g. Understanding how to correctly perform this operation is essential for solving the problem.
Video consigliato:
Percorso guidato
4:56
Function Composition
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. For the composition of functions, the domain of f o g is determined by the values that g can take and the values that f can accept. Identifying these domains is crucial for ensuring that the composed function is valid.
Video consigliato:
Percorso guidato
3:51Domain Restrictions of Composed Functions
Square Root Function
The square root function, denoted as f(x) = √x, is defined only for non-negative values of x. This means that for f to be valid, the input must be greater than or equal to zero. Understanding the restrictions imposed by the square root function is vital for determining the overall domain of the composed function f o g.
Video consigliato:
Percorso guidato
02:20Imaginary Roots with the Square Root Property
Pratica correlata
Domanda del libro di testo
Use the graph of g to solve Exercises 71–76.
Find g(-4)
1089
views
Domanda del libro di testo
Begin by graphing the square root function, f(x) = √x. Then use transformations of this graph to graph the given function. h(x)=-√(x + 1)
844
views
Domanda del libro di testo
Graph both equations in the same rectangular coordinate system and find all points of intersection. Then show that these ordered pairs satisfy the equations. (x − 2)²+(y+3)² = 4, y = x - 3
888
views
Domanda del libro di testo
Begin by graphing the square root function, f(x) = √x. Then use transformations of this graph to graph the given function. g(x) = √(x+1)
814
views
Domanda del libro di testo
Use the graph of g to solve Exercises 71–76.
Find g(2)
112
views