Explanation Given: The functions f ( x ) = | x | and g ( θ ) = sin ( θ ) . Key concepts used: Composition of two functions is defined as: ⇒ f ∘ g ( x ) = f ( g ( x ) ) ⇒ g ∘ f ( x ) = g ( f ( x ) ) While finding domain of a composite function, restrictions on the composite function as well as restrictions on inner function are taken into account. Calculation: First of all, we find composite functions as shown below: ⇒ f ∘ g = f ( g ) ⇒ f ∘ g = f ( sin ( θ ) ) ⇒ f ∘ g = | sin ( θ ) | This is sine function, so domain is all real numbers. Inner function g ( θ ) = sin ( θ ) is sine function, so there are no restrictions on this either

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 1.3, Problem 30E

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Composite functions f∘g and g∘f and their domains.

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Chapter 1.3, Problem 29E

Chapter 1.3, Problem 31E

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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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Composite functions f ∘ g and g ∘ f and their domains.

Solution Summary: The author explains how to determine the composite functions and their domains. The domain of the two functions is (-infty)

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Composite functions f∘g and g∘f and their domains.

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Chapter 1 Solutions