a. Explanation Given information: It is given in the question that the function be f ( x ) = 1 − x 2 , 0 ≤ x ≤ 1. Concept Used: In this we have to know about the concept of inverse of function. Calculation: f ( x ) = 1 − x 2 , 0 ≤ x ≤ 1 f ( 0 ) = 1 − 0 2 = 1 f ( 1 ) = 1 − 1 2 = 0 Domain of f is [ 0 , 1 ] and range is [ 0 , 1 ] Let y = f ( x ) = 1 − x 2 and solve for x y 2 = 1 − x 2 x 2 = 1 − y 2 Solving for x x = 1 − y 2 = f − 1 ( y ) Take the positive root only because y ∈ [ 0 , 1 ] b. To determine Draw the graph of f and explain it.

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Question

Chapter 1.5, Problem 31E

To determine

Find f−1 . Define the relation between f−1 andf .

To determine

Draw the graph of f and explain it.

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Chapter 1.5, Problem 30E

Chapter 1.5, Problem 32E

Chapter 1 Solutions

Biocalculus

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

Ch. 1.1 - Prob. 11E Ch. 1.1 - Prob. 12E Ch. 1.1 - Prob. 13E Ch. 1.1 - Prob. 14E Ch. 1.1 - Prob. 15E Ch. 1.1 - Prob. 16E Ch. 1.1 - Prob. 17E Ch. 1.1 - Prob. 18E Ch. 1.1 - Prob. 19E Ch. 1.1 - Prob. 20E Ch. 1.1 - Prob. 21E Ch. 1.1 - Prob. 22E Ch. 1.1 - Prob. 23E Ch. 1.1 - Prob. 24E Ch. 1.1 - Prob. 25E Ch. 1.1 - Prob. 26E Ch. 1.1 - Prob. 27E Ch. 1.1 - Prob. 28E Ch. 1.1 - Prob. 29E Ch. 1.1 - Prob. 30E Ch. 1.1 - Prob. 31E Ch. 1.1 - Prob. 32E Ch. 1.1 - Prob. 33E Ch. 1.1 - Prob. 34E Ch. 1.1 - Prob. 35E Ch. 1.1 - Prob. 36E Ch. 1.1 - Prob. 37E Ch. 1.1 - Prob. 38E Ch. 1.1 - Prob. 39E Ch. 1.1 - Prob. 40E Ch. 1.1 - Prob. 41E Ch. 1.1 - Prob. 42E Ch. 1.1 - Prob. 43E Ch. 1.1 - Prob. 44E Ch. 1.1 - Prob. 45E Ch. 1.1 - Prob. 46E Ch. 1.1 - Prob. 47E Ch. 1.1 - Prob. 48E Ch. 1.1 - Prob. 49E Ch. 1.1 - Prob. 50E Ch. 1.1 - Prob. 51E Ch. 1.1 - Prob. 52E Ch. 1.1 - Prob. 53E Ch. 1.1 - Prob. 54E Ch. 1.1 - Prob. 55E Ch. 1.1 - Prob. 56E Ch. 1.1 - Prob. 57E Ch. 1.1 - Prob. 58E Ch. 1.1 - Prob. 59E Ch. 1.1 - Prob. 60E Ch. 1.1 - 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Find f − 1 . Define the relation between f − 1 andf .

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Find f−1 . Define the relation between f−1 andf .

Draw the graph of f and explain it.

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Chapter 1 Solutions