How to determine if a function is odd or even

[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?

 

[Gokul43201]

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?

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.

 

[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?

 

[Gokul43201]

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?

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.

 

[arildno]

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

 

[UrbanXrisis]

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

 

[Gokul43201]

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

 

[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)]

 

[Gokul43201]

Read post #5.

 

[UrbanXrisis]

I get the point thanks

 

[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?