Hey,

I'm just going to use this to do some mathematics to send to a very special person

, basically hogging your equation software thing. Just to make it useful, I'll explain what is to be done.

Basically what we're doing here is finding out if a function is even or odd.

If $\displaystyle f(-x) = -f(x)$ then the function is odd.

If $\displaystyle f(-x) = f(x)$ then the function is even.

If $\displaystyle f(-x) \neq f(x)$ or $\displaystyle f(-x) \neq -f(x)$ then the function is neither even or odd.

An example:

Say we have

$\displaystyle f(x) = x^2/\sqrt{x^2-1}$

To find out if it's odd or even we find $\displaystyle f(-x)$

Which is

$\displaystyle

f(-x) = (-x)^2/\sqrt{(-x)^2-1}

$

so

$\displaystyle

f(-x) = x^2/\sqrt{x^2-1}

$

which means

$\displaystyle

f(-x) = f(x)

$

So that means the function

$\displaystyle f(x) = x^2/\sqrt{x^2-1}$

Is even because $\displaystyle f(-x) = f(x)$