a. Explanation Given information: p is a function that is defined for all x . Function f is defined by f ( x ) = p ( x ) + p ( − x ) . Concepts used: 1. ) A function f is even if f ( − x ) = f ( x ) . Graph of an even function is symmetric about y − axis. 2. ) A function f is odd if f ( − x ) = − f ( x ) . Graph of an odd function is symmetric about origin. Calculation: Given function is, p is a function that is defined for all x . Function f is defined by , f ( x ) = p ( x ) + p ( − x ) ....eq(i) Let us first calculate f ( − x ) b. To determine Whether given function f ( x ) = p ( x ) − p ( − x ) is an odd function.

4th Edition

ISBN: 9781319055844

Author: FRANZOSA

Publisher: VST

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Question

Chapter 1.1, Problem 68E

To determine

Whether given function f(x)=p(x)+p(−x) is an even function.

To determine

Whether given function f(x)=p(x)−p(−x) is an odd function.

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Chapter 1.1, Problem 67E

Chapter 1.1, Problem 69E

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Chapter 1 Solutions

EBK CALCULUS

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Whether given function f ( x ) = p ( x ) + p ( − x ) is an even function.

Solution Summary: The author explains that p is a function that is defined for all x.