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Question The speed, V (km/h), of a car at time t (seconds) is given by. where 0 ≤t ≤ 150. 75 + 30sin (л(t-75) 150 V = f(t) 2- sin (π(t-75) 150 a) We want to know when the car will reach speed. Solve for the time t in terms of the speed V, and hence find the formula for the inverse function ƒ¯¹(t). b) Write down the domain of f¯¹(t). c) Plot f(t) from t = 0 to t = 150 and then plot f¯¹(t) on the same axes but only for the values of t in the domain of the inverse function found in (b).

Question The speed, V (km/h), of a car at time t (seconds) is given by. where 0 ≤t ≤ 150. 75 + 30sin (л(t-75) 150 V = f(t) 2- sin (π(t-75) 150 a) We want to know when the car will reach speed. Solve for the time t in terms of the speed V, and hence find the formula for the inverse function ƒ¯¹(t). b) Write down the domain of f¯¹(t). c) Plot f(t) from t = 0 to t = 150 and then plot f¯¹(t) on the same axes but only for the values of t in the domain of the inverse function found in (b).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.1: Inverse Functions
Problem 55E
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Question The speed, V (km/h), of a car at time t (seconds) is given by. where 0 ≤t ≤ 150. 75 + 30sin (л(t-75) 150 V = f(t) 2- sin (π(t-75) 150 a) We want to know when the car will reach speed. Solve for the time t in terms of the speed V, and hence find the formula for the inverse function f¯¹(t). b) Write down the domain of f¯¹(t). c) Plot f(t) from t = 0 to t = 150 and then plot f¯¹(t) on the same axes but only for the values of t in the domain of the inverse function found in (b).
Transcribed Image Text:Question The speed, V (km/h), of a car at time t (seconds) is given by. where 0 ≤t ≤ 150. 75 + 30sin (л(t-75) 150 V = f(t) 2- sin (π(t-75) 150 a) We want to know when the car will reach speed. Solve for the time t in terms of the speed V, and hence find the formula for the inverse function f¯¹(t). b) Write down the domain of f¯¹(t). c) Plot f(t) from t = 0 to t = 150 and then plot f¯¹(t) on the same axes but only for the values of t in the domain of the inverse function found in (b).
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d) Describe the geometric relationship that you can see when you consider both f(t) and f-¹(t). e) When will the speed of the car be equal to 60km/h? Use the inverse function you found in part (a) to help you answer this.
Transcribed Image Text:d) Describe the geometric relationship that you can see when you consider both f(t) and f-¹(t). e) When will the speed of the car be equal to 60km/h? Use the inverse function you found in part (a) to help you answer this.
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This is Parts b and c of the same question.

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b) Write down the domain of f¨¹(t). c) Plot f(t) from t = 0 to t = 150 and then plot f-1(t) on the same axes but only for the values of t in the domain of the inverse function found in (b).
Transcribed Image Text:b) Write down the domain of f¨¹(t). c) Plot f(t) from t = 0 to t = 150 and then plot f-1(t) on the same axes but only for the values of t in the domain of the inverse function found in (b).
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