Explanation Given information: The surface area S of a sphere of radius r is given by S ( r ) = 4 π r 2 . Formula used: Inverse: - Let f have domain D and range R. If there is a function g with domain R such that g ( f ( x ) ) = x for x ∈ D and f ( g ( x ) ) = x for x ∈ R then f is said to be invertible. Square root identity x y = x y Rationalization: - denominator should not be irrational and fixing by making the denominator rational to be in “Simplest Form” is called Rationalizing the Denominator. Calculation: y = 4 π r 2 r 2 = 4 π y r = 4 π y r = 2 π y So, the inverse is r = S − 1 ( r ) , y → r S − 1 ( r ) = 2 π

4th Edition

ISBN: 9781319309671

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 1.5, Problem 10E

To determine

Find the inverse of S(r), expressing r as a function of S if S(r)=4πr2.

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Chapter 1.5, Problem 9E

Chapter 1.5, Problem 11E

Chapter 1 Solutions

CALCULUS: EARLY TRANS 4TH ED W/ ACCESS

Ch. 1.1 - Prob. 1PQ Ch. 1.1 - Prob. 2PQ Ch. 1.1 - Prob. 3PQ Ch. 1.1 - Prob. 4PQ Ch. 1.1 - Prob. 5PQ Ch. 1.1 - Prob. 6PQ Ch. 1.1 - Prob. 7PQ Ch. 1.1 - Prob. 8PQ Ch. 1.1 - Prob. 9PQ Ch. 1.1 - Prob. 10PQ

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Find the inverse of S ( r ) , expressing r as a function of S if S ( r ) = 4 π r 2 .

Solution Summary: The author explains how to find the inverse of S(r), expressing r as a function of the denominator.

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Find the inverse of S(r), expressing r as a function of S if S(r)=4πr2.

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Chapter 1 Solutions