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Symmetry question

  • Thread starter Nitrate
  • Start date
  • #1
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Homework Statement


is the function f(x) = (2x^2-x)/(x^2+x) even, odd, or neither?


Homework Equations



f(-x)=f(x) = even
f(-x)=-f(x) = odd
f(-x)≠f(x)≠ -f(x)

The Attempt at a Solution


f(x) = (2x^2-x)/(x^2+x)
f(-x)=(2(-x)^2+x)/((-x)^2+(-x))
f(-x) = (2x^2+x)/(x^2-x)

i think thats the right way to do it, but i don't know if it's even or odd.
 

Answers and Replies

  • #2
CompuChip
Science Advisor
Homework Helper
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That is the right way to do it.
So you have found the explicit form of f(-x).
Now is that equal to f(x), to -f(x), or neither?
 
  • #3
ehild
Homework Helper
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Just try to substitute some value for x, say x=2 and x=-2. If f(2) is not equal either to f(-2) or -f(-2) than the function is neither odd nor even.

ehild
 
  • #4
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judging that the signage is switched from the original function to the f(-x) and the square terms stayed the same, then the function is even?
 
  • #5
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Just try to substitute some value for x, say x=2 and x=-2. If f(2) is not equal either to f(-2) or -f(-2) than the function is neither odd nor even.

ehild
never saw it that way. thanks :)
 
  • #6
HallsofIvy
Science Advisor
Homework Helper
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932
While you can use that "counter-example" method to prove that a function is neither even nor odd (and most functions are), you cannot use it to prove a function is either even or odd. The fact that f(2)= f(-2) does NOT prove it happens for all x.
 

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