# Symmetry question

## 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.

CompuChip
Homework Helper
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?

ehild
Homework Helper
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

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?

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 :)

HallsofIvy