Explanation Given: f ( x ) and g ( x ) are two given function. Formula used: sin ( − x ) = − sin x Calculation: f ( x ) and g ( x ) are two even function. f ( − x ) = f ( x ) g ( − x ) = g ( x ) Consider the functional equation z ( x ) = f ( x ) + g ( x ) . z ( − x ) = f ( − x ) + g ( − x ) z ( − x ) = f ( x ) + g ( x ) z ( − x ) = z ( x ) Therefore, z ( x ) is an even function. This shows that the sum of two even functions is always an even function. f ( x ) and g ( x ) are odd function. f ( − x ) = − f ( x ) g ( − x ) = − g ( x ) Consider the functional equation z ( x ) = f ( x ) + g ( x )

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Chapter 1.1, Problem 73E

To determine

The sum of two functions according to the given conditions.

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Chapter 1.1, Problem 72E

Chapter 1.1, Problem 74E

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Chapter 1 Solutions

Biocalculus

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The sum of two functions according to the given conditions.

Solution Summary: The author explains that the sum of two functions according to the given conditions is always an even function.

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The sum of two functions according to the given conditions.

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Chapter 1 Solutions