Explanation Given information: f ( x ) = 5 e x + 8 e − x Formula used: cosh x = e x + e − x 2 sinh x = e x − e − x 2 Calculation: f ( x ) = 2 f ( x ) 2 [ ∵ multiplying and dividing by two ] = 1 2 [ f ( x ) + f ( x ) ] = 1 2 [ f ( x ) + f ( x ) − f ( − x ) + f ( − x ) ] [ ∵ adding and subtrating with f ( − x ) ] = f ( x ) + f ( − x ) 2 + f ( x ) − f ( − x ) 2 So, f ( x ) = f ( x ) + f ( − x ) 2 = Even function f ( x ) = f ( x ) − f ( − x ) 2 = Odd function cosh x = e x + e − x 2

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

4th Edition

ISBN: 9781319312886

Author: Rogawski, Jon, Adams, Colin, FRANZOSA, Robert

Publisher: W. H. Freeman

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Chapter 1.6, Problem 53E

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Prove thatevery function f can be written as a sum in the form f(x)=f+(x)+f−(x) where f+(x) is an even function and f−(x) is an odd function and also express f(x)=5ex+8e−x in terms of coshx and sinhx.

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Chapter 1.6, Problem 52E

Chapter 1.7, Problem 1PQ

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Chapter 1 Solutions

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

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Prove thatevery function f can be written as a sum in the form f ( x ) = f + ( x ) + f − ( x ) where f + ( x ) is an even function and f − ( x ) is an odd function and also express f ( x ) = 5 e x + 8 e − x in terms of cosh x and sinh x .

Solution Summary: The author demonstrates that every function f can be written as a sum.

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Prove thatevery function f can be written as a sum in the form f(x)=f+(x)+f−(x) where f+(x) is an even function and f−(x) is an odd function and also express f(x)=5ex+8e−x in terms of coshx and sinhx.

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