# Homework Help: I Need Help With A Proof! *very Urgent*

1. Oct 25, 2007

### STAR3URY

1. The problem statement, all variables and given/known data
Prove that if f(x) is both odd and even (functions) then f(x) must be the constant function 0. Basically prove that no other function other than 0, can be both odd and even.

2. Oct 25, 2007

### neutrino

How do you define an odd function and an even function?

3. Oct 25, 2007

### STAR3URY

Odd function is when f(-x) = -f(x) and even is if f(-x) = f(-x)

4. Oct 25, 2007

### neutrino

That's not quite right.

But in a way, that is what you have to use once you have the definitions of both types of functions. :)

5. Oct 26, 2007

### Hurkyl

Staff Emeritus
As neutrino said, you got the definition wrong. Get the definition right, and then you can make progress.

6. Oct 28, 2007

### STAR3URY

f(-x) = f(x) is even

f(-x) = -f(x) is odd

7. Oct 29, 2007

### coomast

The definitions are correct. Now if a function has to fullfill both of these, it fullfills the product. Use this together with the fact that a square is always.... and the fact that something is positive and negative at the same time must be....

8. Oct 29, 2007

### andytoh

Basically f(-x) = -f(-x) i.e. f = -f. The rest is algebra.