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

1. Jan 3, 2005

### akt223

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)

2. Jan 3, 2005

### Dr Transport

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. Jan 3, 2005

### akt223

Alright, I think I get it, thanks.

4. Jan 3, 2005

### HallsofIvy

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. Jan 3, 2005

### rachmaninoff

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