Constructing Even Functions from Odd and Even Functions

[roshan2004]

Homework Statement

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

Homework Equations

f_1(x)=-f_1(-x)
f_2(x)=f_2(-x)

The Attempt at a Solution

 

[Mentallic]

Are there any restrictions to what we can do?

f_1(x)f_2(x) 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.

 

[roshan2004]

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

 

[Mentallic]

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?