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A. Solve for the following word problems. 1. Engineers have determined that the maximum force t in tons that a particular bridge can carry is related to the distance d in meters between its supports by the following function: 3 12.5 t(d) = %3D d How far should the supports be if the bridge is to support 6.5 tons? Construct an inverse function to determine the result. 2. The amount of a commodity that is sold is called the demand for the commodity. The demand D for a certain commodity is a function of the price given by D(p) = -3p + 150 a. Find D-1. What does D-1 b. Find D-(30). What does your answer represent? represent?

A. Solve for the following word problems. 1. Engineers have determined that the maximum force t in tons that a particular bridge can carry is related to the distance d in meters between its supports by the following function: 3 12.5 t(d) = %3D d How far should the supports be if the bridge is to support 6.5 tons? Construct an inverse function to determine the result. 2. The amount of a commodity that is sold is called the demand for the commodity. The demand D for a certain commodity is a function of the price given by D(p) = -3p + 150 a. Find D-1. What does D-1 b. Find D-(30). What does your answer represent? represent?

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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Solve the for the following word problems

 

NO. 1, 2 a. & b. 

Background Infomation: Backoverse of a function is a rule that acts on the output of the function and produces the eresponding input. So the inverse "undoes" or reverses what the function has done. Not all functions have inverses; those that do are called one-to-one. Leaming Competency: M11GM-le-2 - solves problems involving inverse functions M11GM-le-3 - represents real-life situations using exponential functions Mi1GM-le4- distinguishes between exponential function, exponential equation, and exponential inequality Discussion/Examples: Word Problems Involving Inverse Functions Example 1. For his services, a private investigator requires a P25000 retention fee plus P4000 per hour. Let y represent the number of hours the investigator spends working on a case. a. Find a function f that models the investigator's fee as a function of x. b. Find f1. What does f-1 represent? c. Find f-(61000). What does your answer represent? Solution: a. The investigator's fee is f(x) = 25000 + 4000x b. Write the function f as a function of x f(x) = 25000 + 4000x y = 25000 + 4000x x = 25000 + 4000y replace f(x) by y interchange x and y solve for y %3D 4000y x-25000 4000 4000 x-25000 y = express answer in simplest term 4000 1 y = 25 replace y by f-'(x) to get the final answer 4000 4 (x) 25 X - final answer 4000 The function f-(x) represents the number of hours the investigator worked if his payment is x. c. Write the function f-"(x) = 4000 replace x by the given value which is 61000 %3D 1 f-1(61000) f'(61000) = 9 (61000)- 25 4000 4 final answer %3D The function f-(61000) represents the number of hours the investigator worked if his payment is P61000. Example 2. The relationship between the Fahrenheit (F) and Celsius (C) scales is given by 9. F(C) = =C + 32 a. Find F-1. What does F-1 represent? b. Find F-1(86). What does your answer represent? Solution: The solution is basically the same with the solution in Example 1, but take note of this: do not interchange F and C to avoid confusion, because they represent specific values. a. Write the function F as a function of C F =C + 32 F - 32 = C (F – 32) (;) = (¿c) () C = (F – 32) () C is the inverse function of the original given function F =C + 32, so we can say that C = F-1. It solve for C, transpose 32 on the other side multiply both sides by %3D final answer %3D represents the temperature in degrees in Celsius given a temperature F in degrees Fahrenheit. Page 1 of 4
Transcribed Image Text:Background Infomation: Backoverse of a function is a rule that acts on the output of the function and produces the eresponding input. So the inverse "undoes" or reverses what the function has done. Not all functions have inverses; those that do are called one-to-one. Leaming Competency: M11GM-le-2 - solves problems involving inverse functions M11GM-le-3 - represents real-life situations using exponential functions Mi1GM-le4- distinguishes between exponential function, exponential equation, and exponential inequality Discussion/Examples: Word Problems Involving Inverse Functions Example 1. For his services, a private investigator requires a P25000 retention fee plus P4000 per hour. Let y represent the number of hours the investigator spends working on a case. a. Find a function f that models the investigator's fee as a function of x. b. Find f1. What does f-1 represent? c. Find f-(61000). What does your answer represent? Solution: a. The investigator's fee is f(x) = 25000 + 4000x b. Write the function f as a function of x f(x) = 25000 + 4000x y = 25000 + 4000x x = 25000 + 4000y replace f(x) by y interchange x and y solve for y %3D 4000y x-25000 4000 4000 x-25000 y = express answer in simplest term 4000 1 y = 25 replace y by f-'(x) to get the final answer 4000 4 (x) 25 X - final answer 4000 The function f-(x) represents the number of hours the investigator worked if his payment is x. c. Write the function f-"(x) = 4000 replace x by the given value which is 61000 %3D 1 f-1(61000) f'(61000) = 9 (61000)- 25 4000 4 final answer %3D The function f-(61000) represents the number of hours the investigator worked if his payment is P61000. Example 2. The relationship between the Fahrenheit (F) and Celsius (C) scales is given by 9. F(C) = =C + 32 a. Find F-1. What does F-1 represent? b. Find F-1(86). What does your answer represent? Solution: The solution is basically the same with the solution in Example 1, but take note of this: do not interchange F and C to avoid confusion, because they represent specific values. a. Write the function F as a function of C F =C + 32 F - 32 = C (F – 32) (;) = (¿c) () C = (F – 32) () C is the inverse function of the original given function F =C + 32, so we can say that C = F-1. It solve for C, transpose 32 on the other side multiply both sides by %3D final answer %3D represents the temperature in degrees in Celsius given a temperature F in degrees Fahrenheit. Page 1 of 4
A. Solve for the following word problems. 1. Engineers have determined that the maximum force t in tons that a particular bridge can carry is related to the distance d in meters between its supports by the following function: 3 12.5 e(d) = () %3D How far should the supports be if the bridge is to support 6.5 tons? Construct an inverse function to determine the result. 2. The amount of a commodity that is sold is called the demand for the commodity. The demandD for a certain commodity is a function of the price given by D(p) = -3p + 150 %3D a. Find D-1. What does D-1 represent? b. Find D-(30). What does your answer represent? -1,
Transcribed Image Text:A. Solve for the following word problems. 1. Engineers have determined that the maximum force t in tons that a particular bridge can carry is related to the distance d in meters between its supports by the following function: 3 12.5 e(d) = () %3D How far should the supports be if the bridge is to support 6.5 tons? Construct an inverse function to determine the result. 2. The amount of a commodity that is sold is called the demand for the commodity. The demandD for a certain commodity is a function of the price given by D(p) = -3p + 150 %3D a. Find D-1. What does D-1 represent? b. Find D-(30). What does your answer represent? -1,
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