Constructing Even Functions from Odd and Even Functions

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Homework Help Overview

The discussion revolves around the construction of an even function from a given odd function and an even function. The original poster presents the problem of how to achieve this using the properties of these functions.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants explore the possibility of using the product of the odd and even functions, questioning whether this product remains odd. There is also consideration of squaring the product to obtain an even function, with some uncertainty about whether this approach meets the original poster's requirements.

Discussion Status

The discussion is active, with participants engaging in reasoning about the properties of odd and even functions. Some guidance is offered regarding the implications of squaring the product, but there is no consensus on whether this is sufficient or if additional steps are needed.

Contextual Notes

Participants note the absence of restrictions on the operations performed with the functions, which may influence their reasoning and exploration of potential solutions.

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Homework Statement


Let [tex]f_1(x)[/tex] and [tex]f_2(x)[/tex] be odd and even functions respectively. How can we construct an even function out of these?


Homework Equations


[tex]f_1(x)=-f_1(-x)[/tex]
[tex]f_2(x)=f_2(-x)[/tex]


The Attempt at a Solution


 
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Are there any restrictions to what we can do?

[tex]f_1(x)f_2(x)[/tex] would be an odd function, can you show why?

Then we could supposedly square the entire thing and end up with an even function... But I don't know exactly what you're looking for.
 


No, there are no restrictions to what we can do.
yes, I can see that it is an odd function since it gives me-
[tex] -f_1(-x)f_2(-x)[/tex]
 


roshan2004 said:
No, there are no restrictions to what we can do.

Right, so is squaring the product of the functions enough here, or are you looking for something more?
 

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