Answered: Prove that all functions can be written…

Math

Calculus

Prove that all functions can be written as a sum of an even function and an odd function

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.7: Operations On Functions

Problem 42E

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Question

Prove that all functions can be written as a sum of an even function and an odd function

Expert Solution

Step 1

Show that: $w (x) = u (x) + v (x)$

and also show that: $u (x)$ is even and v(x) is odd,

Step by step

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