Question

How do you determine if `xy=1` is an even or odd function?

Answer 1

I'm assuming that `y` is a function of `x`, so `y(x)=1/x`. This function is odd.

Explanation:

The easiest way to determine whether a function is even or odd is to evaluate `y(-x)` in terms of `y(x)`, e.g.
`y(-x)=1/(-x)=-(1/x)=-y(x)`
and from the condition `y(-x)=y(x)` we see that our function is odd.

To fully understand this problem let's look at an example of an even function: `y(x)=x^2`.
`y(-x)=(-x)^2=x^2=y(x)`
Here, since `y(-x)=y(x)` this function is even.

Important notice: some functions, unlike integers, can be both odd and even (e.g. `y(x)=0`) or neither odd nor even (e.g. `y(x)=x+1`).