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 )

Bundle: Biocalculus: Calculus, Probability, And Statistics For The Life Sciences + Webassign Printed Access Card For Stewart/day's Biocalculus: Calculus For Life Sciences, 1st Edition, Multi-term

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ISBN: 9781305779037

Author: James Stewart, Troy Day

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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Bundle: Biocalculus: Calculus, Probability, And Statistics For The Life Sciences + Webassign Printed Access Card For Stewart/day's Biocalculus: Calculus For Life Sciences, 1st Edition, Multi-term

Ch. 1.1 - Prob. 1E Ch. 1.1 - Prob. 2E Ch. 1.1 - Prob. 3E Ch. 1.1 - Prob. 4E Ch. 1.1 - Prob. 5E Ch. 1.1 - Prob. 6E Ch. 1.1 - Prob. 7E Ch. 1.1 - Prob. 8E Ch. 1.1 - Prob. 9E Ch. 1.1 - Prob. 10E

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OTHER APPLICATION Attitude Change Social psychologist have found that as the discrepancy between the view of a speaker and those of an audience increase to a point but decrease when the discrepancy becomes too large particular if the communicator is viewed by the audience as having low credibility, Suppose that the degree of change can be approximated by the function D(x)=x4+8x3+80x2 Where x is the discrepancy between the view of the speaker and those of the audience as measure by score on a question-naira. Find the amount of discrepancy the speaker should aim for to maximize the attitude change in the audience. Source: Journal of Personality and Social Psychology.

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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