# Odd vs even

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?

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Gokul43201
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UrbanXrisis said:
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.

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
Staff Emeritus
Gold Member
UrbanXrisis said:
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
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Plug in -x at the x place. If what comes out of f(-x) is EXACTLY -f(x), then your function is odd.

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

Gokul43201
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$f(x) = x^3 + x^2$ is neither odd nor even, (this is what your example simplifies to). See why this is true, by applying the definition.

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
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