Let S = f(r) = 4pir^2 be a function whose input (r) is the radius of a sphere (in inches) andwhose 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 f 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-*(200) is such a number r, that= 200g) Based on part f) write the general statement about an inverse f-'(question is fully continued and clear in the image attached) Q2. Let S = f(r) = 47² be a function whose input (r) is the radius of a sphere (in inches) andwhose 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 contextof 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 thesentencef-¹(200) is such a number r, that= 200g) Based on part f) write the general statement about an inverse f-¹fis such a number r, that_

Since you have posted a multiple subparts question according to guidelines I will solve first(a,b,c)…

Answered: Q2. Let S = f(r) = 4m² be a function…

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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Let S = f(r) = 4pir^2 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 f 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-*(200) is such a number r, that = 200 g) Based on part f) write the general statement about an inverse f-'(question is fully continued and clear in the image attached)