Explanation Formula used: A function f is an even function if f ( − x ) = f ( x ) . A function f is an odd function if f ( − x ) = − f ( x ) . Calculation: Let the two even functions f ( x ) and g ( x ) such that f ( x ) = f ( − x ) and g ( x ) = g ( − x ) . Add the two even functions. h ( − x ) = f ( − x ) + g ( − x ) = f ( x ) + g ( x ) = h ( x ) Thus, h ( − x ) = h ( x )

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 1.1, Problem 79E

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Prove that the sum of two even functions is even and the sum of two odd functions is odd.

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Chapter 1.1, Problem 78E

Chapter 1.1, Problem 80E

Chapter 1 Solutions

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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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Prove that the sum of two even functions is even and the sum of two odd functions is odd.

Solution Summary: The author explains that the sum of two even functions is even, and the addition of one odd function is odd.

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Prove that the sum of two even functions is even and the sum of two odd functions is odd.

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Chapter 1 Solutions