Domanda del libro di testo
Let f and g be defined by the following table: Find
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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 93
Let f(x) = x² − x + 4 and g(x) = 3x – 5. Find g (1) and f(g(1)).
Guida verificata passo dopo passo1
First, identify the given functions: \(f(x) = x^{2} - x + 4\) and \(g(x) = 3x - 5\).
Calculate \(g(1)\) by substituting \(x = 1\) into the function \(g(x)\): \(g(1) = 3(1) - 5\).
Simplify the expression for \(g(1)\) to find its value.
Next, find \(f(g(1))\) by substituting the value of \(g(1)\) into the function \(f(x)\): \(f(g(1)) = (g(1))^{2} - g(1) + 4\).
Simplify the expression for \(f(g(1))\) by squaring \(g(1)\), subtracting \(g(1)\), and then adding 4 to get the final expression.
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Function Evaluation
Function evaluation involves substituting a specific input value into the function's formula to find the corresponding output. For example, to find g(1), replace x with 1 in g(x) = 3x - 5 and simplify.
Video consigliato:
4:26
Evaluating Composed Functions
Composite Functions
A composite function like f(g(1)) means applying one function to the result of another. First, evaluate the inner function g(1), then use that output as the input for the outer function f.
Video consigliato:
4:56Function Composition
Polynomial and Linear Functions
Understanding the types of functions involved helps in evaluation. Here, f(x) is a quadratic polynomial (degree 2), and g(x) is a linear function (degree 1), which affects how you substitute and simplify expressions.
Video consigliato:
06:04Introduction to Polynomial Functions
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