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 ) . 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: 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 ) ....eq(i) Since, p ( a b ) = p ( b ) − p ( a ) ....eq(ii) Therefore, f ( x ) = p ( 2 − x 2 + x ) = p ( 2 + x ) − p ( 2 − x )

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…

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Chapter 1.1, Problem 69E

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Whether given 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 (CLOTH)

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Whether given function f ( x ) = p ( 2 − x 2 + x ) is an odd function.

Solution Summary: The author explains whether given function f(x)=p(ab) is an odd function.

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

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Chapter 1 Solutions