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7. Consider the function f(x)=₂ a. By graphing the function, explain why f is one-to-one. b. Find a formula for the inverse function of f (call this function f-¹). c. What is the value of f¹(f (8))? d. What is the value of f(f-¹(49))?

7. Consider the function f(x)=₂ a. By graphing the function, explain why f is one-to-one. b. Find a formula for the inverse function of f (call this function f-¹). c. What is the value of f¹(f (8))? d. What is the value of f(f-¹(49))?

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.4: Composition Of Functions
Problem 97SE: The number of bacteria in a refrigerated food product is given by N(T)=23T256T+1,3T33 ,where T is...
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7. Consider the function f(x)==-²₂. a. By graphing the function, explain why f is one-to-one. b. Find a formula for the inverse function of f (call this function f-¹). c. What is the value of f-¹(f (8))? d. What is the value of f(f¹(49))? 8. At CheapCo Convenience Stores, employees receive an increase in their hourly wage each year. A certain employee's hourly wage in dollars per hour, t years after she starts working for CheapCo, is given by the formula w(t) = 9.50 +0.30t. a. What is w(10)? What does this value tell us about the employee's hourly wage? b. What is w¹(14)? What does this value tell us about the employee's hourly wage? In real life, why might somebody be interested in finding and understanding the inverse function w ¹7 c.
Transcribed Image Text:7. Consider the function f(x)==-²₂. a. By graphing the function, explain why f is one-to-one. b. Find a formula for the inverse function of f (call this function f-¹). c. What is the value of f-¹(f (8))? d. What is the value of f(f¹(49))? 8. At CheapCo Convenience Stores, employees receive an increase in their hourly wage each year. A certain employee's hourly wage in dollars per hour, t years after she starts working for CheapCo, is given by the formula w(t) = 9.50 +0.30t. a. What is w(10)? What does this value tell us about the employee's hourly wage? b. What is w¹(14)? What does this value tell us about the employee's hourly wage? In real life, why might somebody be interested in finding and understanding the inverse function w ¹7 c.
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