Question

How do you determine if `f(x)=x^2(9-x)^2` is an even or odd function?

Answer 1

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

Explanation:

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

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

In our example, we find:

`f(1) = 1^2(9-1)^2 = 64`

`f(-1) = 1^2(9+1)^2 = 100`

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

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