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Odd vs even

  • #1
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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?
 

Answers and Replies

  • #2
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.
 
  • #3
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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
Gokul43201
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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 [itex]x^ax^b = x^{a+b}[/itex])

Odd powers of a variable are odd functions. And even powers are even functions.
 
  • #5
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.
 
  • #6
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what if a function was...[(x^7)+(x^6)]/(x^4)
 
  • #7
Gokul43201
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[itex]f(x) = x^3 + x^2 [/itex] is neither odd nor even, (this is what your example simplifies to). See why this is true, by applying the definition.
 
  • #8
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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
Gokul43201
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Read post #5.
 
  • #10
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I get the point :smile: thanks
 
  • #11
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What if the function is defined differently at different intervals? How would I then go about finding out whether it's odd or even?
 

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