# Constructin even functions

1. Jul 4, 2010

### roshan2004

1. The problem statement, all variables and given/known data
Let $$f_1(x)$$ and $$f_2(x)$$ be odd and even functions respectively. How can we construct an even function out of these?

2. Relevant equations
$$f_1(x)=-f_1(-x)$$
$$f_2(x)=f_2(-x)$$

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jul 5, 2010

### Mentallic

Re: Functions

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.

3. Jul 5, 2010

### roshan2004

Re: Functions

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

4. Jul 5, 2010

### Mentallic

Re: Functions

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