Question

How do you determine if `f(x) = 1/[(3x^3) - 4]` is an even or odd function?

Answer 1

`f(x)` is neither even nor odd

Explanation:

An even function is one for which `f(-x) = f(x)` for all `x` in its domain.

An odd function is one for which `f(-x) = -f(x)` for all `x` in its domain.

In our example, we find:

`f(1) = 1/(3-4) = 1/(-1) = -1`

`f(-1) = 1/(-3-4) = 1/(-7) = -1/7`

So neither `f(-1) = f(1)` nor `f(-1) = -f(1)`.

So `f(x)` is neither even nor odd.