# Determine whether f is even, odd, or neither?

by akt223
Tags: determine
 P: 2 I've tried looking through my book to see how to do these, but I just can't find it. Any help would be appreciated: 1) f(x) = 2x^5 - 3x^2 +2 2) f(x) = x^3 - x^7 3) f(x) = (1-x^2)/(1+x^2) 4) f(x) = 1/(x+2) Thanks in advance!
 Sci Advisor PF Gold P: 1,454 the definition of an even and an odd function is as follows: $$f(-x) = f(x)$$ is and even function and $$f(-x) = -f(x)$$ is an odd function.
 P: 2 Alright, I think I get it, thanks.
Math
Emeritus
Thanks
PF Gold
P: 38,706

## Determine whether f is even, odd, or neither?

It is also true (easy to prove) that a rational function (polynomial or quotient of polynomials) is even if and only if all exponents of x are even, odd if and only if all exponents of x are odd.

Of course, functions don't always have "exponents"! sin(x) is an odd function and cos(x) is an even function.
P: n/a
 Of course, functions don't always have "exponents"! sin(x) is an odd function and cos(x) is an even function.
But the series expansions precisely consist of only odd-numbered and only even-numbered polynomial terms, respectively. It's quite elegant.

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