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ways: 19. REINFORCE For each of the following function rules, generate a the function, f, and its inverse, g. Then, generate the rule for the inverse in two w directly from the data for the inverse and by algebraic manipulation of the original function rule. If necessary, show that your two inverse rules are equivalent. a. f(x)=100+ 4x

ways: 19. REINFORCE For each of the following function rules, generate a the function, f, and its inverse, g. Then, generate the rule for the inverse in two w directly from the data for the inverse and by algebraic manipulation of the original function rule. If necessary, show that your two inverse rules are equivalent. a. f(x)=100+ 4x

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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**Section: Understanding Inverse Functions** ### Activity Sheet 2: Exploring "The Inverse" **19. Reinforce** For each of the following function rules, generate a table of data describing the function, \( f \), and its inverse, \( g \). Then, generate the rule for the inverse in two ways: directly from the data for the inverse and by algebraic manipulation of the original function rule. If necessary, show that your two inverse rules are equivalent. #### a. \( f(x) = 100 + 4x \) **Instructions:** 1. **Create a Data Table:** - Construct a table showing values of \( x \) and corresponding \( f(x) \). 2. **Determine the Inverse Function:** - Calculate the inverse function \( g(x) \) directly from your data table. - Use algebraic manipulation of the function rule \( f(x) = 100 + 4x \) to find \( g(x) \). 3. **Verify Equivalence:** - Ensure the inverse function rules derived by both methods are equivalent. **Note**: The worksheet provides space for creating tables and practicing calculations to reinforce the understanding of inverse functions. --- **Graph/Diagram Explanation:** There is no graph or diagram provided in the worksheet. The focus is on tabulating data and performing algebraic manipulations as described.
Transcribed Image Text:**Section: Understanding Inverse Functions** ### Activity Sheet 2: Exploring "The Inverse" **19. Reinforce** For each of the following function rules, generate a table of data describing the function, \( f \), and its inverse, \( g \). Then, generate the rule for the inverse in two ways: directly from the data for the inverse and by algebraic manipulation of the original function rule. If necessary, show that your two inverse rules are equivalent. #### a. \( f(x) = 100 + 4x \) **Instructions:** 1. **Create a Data Table:** - Construct a table showing values of \( x \) and corresponding \( f(x) \). 2. **Determine the Inverse Function:** - Calculate the inverse function \( g(x) \) directly from your data table. - Use algebraic manipulation of the function rule \( f(x) = 100 + 4x \) to find \( g(x) \). 3. **Verify Equivalence:** - Ensure the inverse function rules derived by both methods are equivalent. **Note**: The worksheet provides space for creating tables and practicing calculations to reinforce the understanding of inverse functions. --- **Graph/Diagram Explanation:** There is no graph or diagram provided in the worksheet. The focus is on tabulating data and performing algebraic manipulations as described.
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