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-
$$-f_1(-x)f_2(-x)$$

 

[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?