Explanation Given information: p is a function that is defined for all x > 0 and satisfies p ( a b ) = p ( b ) − p ( a ) . Function f is defined by f ( x ) = p ( 2 − x 2 + x ) . Concepts used: 1. ) A function f is even if f ( − x ) = f ( x ) . 2. ) A function f is odd if f ( − x ) = − f ( x ) . Calculation: As per the given information, p is a function that is defined for all x > 0 and satisfies p ( a b ) = p ( b ) − p ( a ) . Function f is defined by, f ( x ) = p ( 2 − x 2 + x ) … (1) Since, p ( a b ) = p ( b ) − p ( a ) ...(2) Therefore, by equation (2), f ( x ) = p ( 2 − x 2 + x ) = p ( 2 + x ) − p ( 2 − x )

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Question

Chapter 1.1, Problem 69E

To determine

To prove:

The function f(x)=p(2−x2+x) is an odd function.

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Chapter 1.1, Problem 68E

Chapter 1.1, Problem 70E

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Chapter 1 Solutions

Calculus: Early Transcendentals

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