Explanation Given Information: The provided function is f ( x ) = 1 − x x and the inverse function is f − 1 ( x ) = 1 x + 1 . Formula used: The composition of two functions f ( x ) and f − 1 ( x ) is ( f − 1 ∘ f ) ( x ) = f − 1 ( f ( x ) ) and ( f ∘ f − 1 ) ( x ) = f ( f − 1 ( x ) ) . If a function f ( x ) is one-to-one, then f − 1 ( x ) is the unique function such that ( f ∘ f − 1 ) ( x ) = x and ( f − 1 ∘ f ) ( x ) = x . Proof: Consider the provided function f ( x ) = 1 − x x , And the inverse function is f − 1 ( x ) = 1 x + 1 . Since, for a one-to-one function f ( x ) , the inverse is f − 1 ( x ) , such that, ( f − 1 ∘ f ) ( x ) = x and ( f ∘ f − 1 ) ( x ) = x For, the function f ( x ) = 1 − x x </

Intermediate Algebra, Books a la Carte Edition, Plus MyLab Math -- Access Card Package (13th Edition)

13th Edition

ISBN: 9780134679884

Author: Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

Publisher: PEARSON

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Chapter 8.2, Problem 55ES

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To prove: The inverse of the function f(x)=1−xx is f−1(x)=1x+1.

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Chapter 8.2, Problem 54ES

Chapter 8.2, Problem 56ES

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Chapter 8 Solutions

Intermediate Algebra, Books a la Carte Edition, Plus MyLab Math -- Access Card Package (13th Edition)

Ch. 8.1 - Evaluate expressions containing negative...Ch. 8.1 - Prob. 2SR Ch. 8.1 - Prob. 1DE Ch. 8.1 - Prob. 2DE Ch. 8.1 - Prob. 3DE Ch. 8.1 - Prob. 4DE Ch. 8.1 - Prob. 5DE Ch. 8.1 - Prob. 6DE Ch. 8.1 - Prob. 1CCE Ch. 8.1 - Prob. 7DE

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To prove: The inverse of the function f ( x ) = 1 − x x is f − 1 ( x ) = 1 x + 1 .

Solution Summary: The author explains that the inverse of the function f(x)=1-x

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To prove: The inverse of the function f(x)=1−xx is f−1(x)=1x+1.

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Chapter 8 Solutions