Question

How do you determine if `f(x)= x /( x^2 - 1)` is an even or odd function?

Answer 1

Find `f(-x) = -f(x)`, so `f(x)` is an odd function.

Explanation:

An even function satisfies: `f(-x) = f(x)` for all `x` in the domain.

An odd function satisfies: `f(-x) = -f(x)` for all `x` in the domain.

In our example we find:

`f(-x) = (-x)/((-x)^2-1) = -(x/(x^2-1)) = -f(x)`

So `f(x)` is an odd function.