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Q2. Let S = f(r) = 47² be a function whose input (r) is the radius of a sphere (in inches) and whose output (S) is the surface area of the sphere. a) What is the domain of this function? b) Function f has the inverse. Explain why. c) Describe what f¹ does, that is explain what the inputs and outputs are in the context of the question.

Q2. Let S = f(r) = 47² be a function whose input (r) is the radius of a sphere (in inches) and whose output (S) is the surface area of the sphere. a) What is the domain of this function? b) Function f has the inverse. Explain why. c) Describe what f¹ does, that is explain what the inputs and outputs are in the context of the question.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Q2. Let S= f(r) = 4m² be a function whose input (r) is the radius of a sphere (in inches) and whose output (S) is the surface area of the sphere. a) What is the domain of this function? b) Function f has the inverse. Explain why. c) Describe what f¹ does, that is explain what the inputs and outputs are in the context of the question. d) Describe, in words the meaning of f-1 (200) and evaluate the value. e) Explain what it means to solve the equation f(r): = 200? f) Compare the answers to d) and e). What's your conclusion? Write it by completing the sentence f-¹(200) is such a number r, that = 200 g) Based on part f) write the general statement about an inverse ƒ¯¹ f¹__) is such a number r, that_
Transcribed Image Text:Q2. Let S= f(r) = 4m² be a function whose input (r) is the radius of a sphere (in inches) and whose output (S) is the surface area of the sphere. a) What is the domain of this function? b) Function f has the inverse. Explain why. c) Describe what f¹ does, that is explain what the inputs and outputs are in the context of the question. d) Describe, in words the meaning of f-1 (200) and evaluate the value. e) Explain what it means to solve the equation f(r): = 200? f) Compare the answers to d) and e). What's your conclusion? Write it by completing the sentence f-¹(200) is such a number r, that = 200 g) Based on part f) write the general statement about an inverse ƒ¯¹ f¹__) is such a number r, that_
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