ExerciseS 49 to 64, evaluate each composite functIon vhere f(x) = 2x + 3, g(x) = x² – 5x, and h(x) = 4 – 3x?. - -
ExerciseS 49 to 64, evaluate each composite functIon vhere f(x) = 2x + 3, g(x) = x² – 5x, and h(x) = 4 – 3x?. - -
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Question
!["62. \((f \circ g)(3k)\)"
This notation represents the composition of functions \(f\) and \(g\), evaluated at \(3k\). In mathematical terms, this is read as "f of g of \(3k\)".
In function composition, \(g\) is first applied to the input \(3k\), and then the result of that application is used as the input for the function \(f\). This can be formally written as:
\[ (f \circ g)(x) = f(g(x)) \]
Thus, evaluating \((f \circ g)(3k)\) involves the following steps:
1. Compute \(g(3k)\).
2. Use the result from step 1 as the input for the function \(f\) to compute \(f(g(3k))\).
This concept is fundamental in understanding how composite functions work and is useful in various fields such as calculus, engineering, and computer science."](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe91e659-0274-4af0-b893-ea272a52ff02%2Fa07c732c-985a-4463-b06d-5b7272c83a8a%2Fxfrcaa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:"62. \((f \circ g)(3k)\)"
This notation represents the composition of functions \(f\) and \(g\), evaluated at \(3k\). In mathematical terms, this is read as "f of g of \(3k\)".
In function composition, \(g\) is first applied to the input \(3k\), and then the result of that application is used as the input for the function \(f\). This can be formally written as:
\[ (f \circ g)(x) = f(g(x)) \]
Thus, evaluating \((f \circ g)(3k)\) involves the following steps:
1. Compute \(g(3k)\).
2. Use the result from step 1 as the input for the function \(f\) to compute \(f(g(3k))\).
This concept is fundamental in understanding how composite functions work and is useful in various fields such as calculus, engineering, and computer science."
Transcribed Image Text:**Composite Function Exercises:**
In Exercises 49 to 64, evaluate each composite function, where \( f(x) = 2x + 3 \), \( g(x) = x^2 - 5x \), and \( h(x) = 4 - 3x^2 \).
When examining composite functions, you'll combine the given functions in various ways to evaluate them. For example, finding \( f(g(x)) \) involves substituting \( g(x) \) into \( f(x) \). Make sure to follow the function compositions carefully to obtain the correct results.
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