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 89
Capitolo 3, Problema 89

Express the given function h as a composition of two functions f and g so that h(x) = (f ○ g)(x). h(x) = (x2 + 2x - 1)4

Guida verificata passo dopo passo
1
Identify the outer function and the inner function in the expression \(h(x) = (x^2 + 2x - 1)^4\). The outer function is the one applied last, which in this case is raising to the 4th power.
Define the inner function \(g(x)\) as the expression inside the parentheses: \(g(x) = x^2 + 2x - 1\).
Define the outer function \(f(x)\) as the function that raises its input to the 4th power: \(f(x) = x^4\).
Express \(h(x)\) as a composition of \(f\) and \(g\): \(h(x) = (f \circ g)(x) = f(g(x))\).
Verify by substituting \(g(x)\) into \(f\): \(f(g(x)) = (x^2 + 2x - 1)^4\), which matches the original function \(h(x)\).

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:
1m

Concetti 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. If h(x) = (f ○ g)(x), then h(x) = f(g(x)). Understanding this helps in breaking down complex functions into simpler parts.
Video consigliato:
4:56
Function Composition

Identifying Inner and Outer Functions

To express a function as a composition, identify an inner function g(x) that is substituted into an outer function f(x). For h(x) = (x^2 + 2x - 1)^4, the inner function is the expression inside the parentheses, and the outer function raises that result to the fourth power.
Video consigliato:
05:01
Identifying Intervals of Unknown Behavior

Polynomial Functions

Polynomial functions are expressions involving variables raised to whole-number exponents combined using addition, subtraction, and multiplication. Recognizing polynomial structure helps in selecting appropriate f and g functions for composition.
Video consigliato:
06:04
Introduction to Polynomial Functions
Pratica correlata
Domanda del libro di testo

In Exercises 77–92, 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 any; and e. the missing function values, indicated by question marks, below each graph.

130
views
Domanda del libro di testo

In Exercises 77–92, 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 any; and e. the missing function values, indicated by question marks, below each graph.

82
views
Domanda del libro di testo

Begin by graphing the absolute value function, f(x) = |x|. Then use transformations of this graph to graph the given function. h(x) = -|x+3|

1612
views
Domanda del libro di testo

Use the graphs of f and g to solve Exercises 83–90.

Find the domain of ƒ/g.

924
views
1
rank
Domanda del libro di testo

Use the graphs of f and g to solve Exercises 83–90.

Graph f+g.

918
views
Domanda del libro di testo

In Exercises 77–92, 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 any; and e. the missing function values, indicated by question marks, below each graph.

138
views