Question

How do you determine whether `f(x) = (-x+1)(x+2)(x-3)^2` is an odd or even function?

Answer 1

Look at `f(1)` vs `f(-1)` to find that it is neither.

Explanation:

`f(1) = 0` since `(-x+1) = (-1+1) = 0`

`f(-1) != 0` since all the factors are non-zero.

So `f(x)` satisfies neither `f(-x) = f(x)` nor `f(-x) = -f(x)`

So it is neither even nor odd.