Domanda del libro di testo
Find the average rate of change of f(x) = x^2 - 4x from x_1 = 5 to x_2 = 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 53
In Exercises 53–58, f and g are defined by the following tables. Use the tables to evaluate each composite function. f(g(1))
Guida verificata passo dopo passo1
Identify the composite function to evaluate: \(f(g(1))\). This means you first find \(g(1)\), then use that result as the input for \(f\).
Look up the value of \(g(1)\) in the \(g(x)\) table. According to the table, when \(x = 1\), \(g(1) = 1\).
Now, use the value \(g(1) = 1\) as the input for the function \(f\). So, you need to find \(f(1)\).
Look up the value of \(f(1)\) in the \(f(x)\) table. According to the table, when \(x = 1\), \(f(1) = 5\).
Therefore, the value of the composite function \(f(g(1))\) is \(f(1)\), which corresponds to the value found in the previous step.
Concetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Function Evaluation
Function evaluation involves finding the output value of a function for a given input. Using the tables, you locate the input value in the x-column and read the corresponding function value from the f(x) or g(x) column. This is essential for determining values like g(1) or f(g(1)).
Video consigliato:
4:26
Evaluating Composed Functions
Composite Functions
A composite function, denoted as f(g(x)), means applying one function to the result of another. First, evaluate the inner function g at x, then use that output as the input for f. Understanding this process is key to correctly evaluating expressions like f(g(1)).
Video consigliato:
4:56Function Composition
Using Tables to Represent Functions
Tables provide discrete values of functions for specific inputs, allowing evaluation without explicit formulas. By matching input values to outputs in the tables, you can perform operations like composition. This method is useful when functions are defined only by data points.
Video consigliato:
5:31Graphing Rational Functions Using Transformations
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