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Express the function h(z) Your answer is f(2)= Calculator Check Answer 1 in the form fo g. If g(z) = (z + 6), find the function f(z). z+6

Express the function h(z) Your answer is f(2)= Calculator Check Answer 1 in the form fo g. If g(z) = (z + 6), find the function f(z). z+6

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Problem Statement:** Express the function \( h(x) = \frac{1}{x + 6} \) in the form \( f \circ g \). If \( g(x) = (x + 6) \), find the function \( f(x) \). **Solution:** - **Given:** - Function \( h(x) = \frac{1}{x + 6} \) - \( g(x) = x + 6 \) - **Objective:** - Find \( f(x) \) such that \( f(g(x)) = h(x) \). - **Steps:** 1. Identify \( f(x) \) considering \( g(x) = x + 6 \). 2. Since \( h(x) = \frac{1}{x + 6} \), and \( g(x) = x + 6 \), set \( f(g(x)) = \frac{1}{x + 6} \). 3. Therefore, \( f(u) = \frac{1}{u} \) where \( u = x + 6 \). **Answer:** \[ f(x) = \frac{1}{x} \] **Additional Instructions:** - Use the calculator if necessary to verify calculations. - Click "Check Answer" to confirm the solution.
Transcribed Image Text:**Problem Statement:** Express the function \( h(x) = \frac{1}{x + 6} \) in the form \( f \circ g \). If \( g(x) = (x + 6) \), find the function \( f(x) \). **Solution:** - **Given:** - Function \( h(x) = \frac{1}{x + 6} \) - \( g(x) = x + 6 \) - **Objective:** - Find \( f(x) \) such that \( f(g(x)) = h(x) \). - **Steps:** 1. Identify \( f(x) \) considering \( g(x) = x + 6 \). 2. Since \( h(x) = \frac{1}{x + 6} \), and \( g(x) = x + 6 \), set \( f(g(x)) = \frac{1}{x + 6} \). 3. Therefore, \( f(u) = \frac{1}{u} \) where \( u = x + 6 \). **Answer:** \[ f(x) = \frac{1}{x} \] **Additional Instructions:** - Use the calculator if necessary to verify calculations. - Click "Check Answer" to confirm the solution.
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