# Odd vs even

1. Oct 6, 2004

### UrbanXrisis

the rule for an odd function is: -f(x)=f(x) correct?

however, x^3 is odd? Why is that? -(x^3) != (x^3)

Also, how would someone tell if a function is odd or even if it was an equation like: (x^7)(x^6)/(x^4) or something of that nature?

2. Oct 6, 2004

### Gokul43201

Staff Emeritus
You've got the definition wrong. You're essentially stating that -something = something. This is true only if something = 0.

Correct definition : If f(-x) = -f(x), then f is odd.

3. Oct 6, 2004

### UrbanXrisis

ahhh okay! That makes sense! What about telling if a function is odd or even if it was an equation like: (x^7)(x^6)/(x^4) or something similar to that?

4. Oct 6, 2004

### Gokul43201

Staff Emeritus
What you've written can be simplified to x^9. (since $x^ax^b = x^{a+b}$)

Odd powers of a variable are odd functions. And even powers are even functions.

5. Oct 6, 2004

### arildno

Plug in -x at the x place. If what comes out of f(-x) is EXACTLY -f(x), then your function is odd.

6. Oct 6, 2004

### UrbanXrisis

what if a function was...[(x^7)+(x^6)]/(x^4)

7. Oct 6, 2004

### Gokul43201

Staff Emeritus
$f(x) = x^3 + x^2$ is neither odd nor even, (this is what your example simplifies to). See why this is true, by applying the definition.

8. Oct 6, 2004

### UrbanXrisis

Because the exponet is an odd and even number? So it's neither. Does the sign make any difference? Positive or negative? what if a function was...[(x^7)+(x^6)]/[(x^4)-(x^3)]

9. Oct 6, 2004

### Gokul43201

Staff Emeritus

10. Oct 6, 2004

### UrbanXrisis

I get the point thanks

11. Dec 8, 2004

### TSN79

What if the function is defined differently at different intervals? How would I then go about finding out whether it's odd or even?