Explanation Definition Used: Inverse function: Let f be a one-to-one function domain A and range B . Then its inverse function f − 1 has domain B and range A and is defined by f − 1 ( y ) = x ⇔ f ( x ) = y . Property Used: For a one-to-one functionf with domain A and range B and with inverse function f − 1 following properties always holds true. 1. f − 1 ( f ( x ) ) = x for every x in A . 2. f ( f − 1 ( x ) ) = x for every x in B . Horizontal line test: A function is one-to-one if and only if no horizontal line can intersect its graph more than once. It is given that f ( x ) = x 5 + x 3 + x . Now, first step is to verify if this function is one-to-one or not

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Chapter 1.5, Problem 16E

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To find: f−1(3) and f(f−1(2)) where f(x)=x5+x3+x

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Chapter 1.5, Problem 15E

Chapter 1.5, Problem 17E

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Chapter 1 Solutions

Biocalculus

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f − 1 ( 3 ) and f ( f − 1 ( 2 ) ) where f ( x ) = x 5 + x 3 + x

Solution Summary: The author explains that a function is one-to-one if no horizontal line can intersect its graph more than once.

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To find: f−1(3) and f(f−1(2)) where f(x)=x5+x3+x

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Chapter 1 Solutions