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

1. ### akt223

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!

2. ### Dr Transport

1,507
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.

3. ### akt223

2
Alright, I think I get it, thanks.

4. ### HallsofIvy

40,803
Staff Emeritus
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.

5. ### rachmaninoff

0
But the series expansions precisely consist of only odd-numbered and only even-numbered polynomial terms, respectively. It's quite elegant.

Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook

Have something to add?