What happens when x = 1? We have f(1) = (1)^{3}(1) = 0 f(1) = (1)^{3}(1) = 1 + 1 = 0 The function f(x) is even, right? Nope. If we used x instead of the specific number 1 we would find f(x) = x^{3}x f(x) = x^{3} + x. These aren't the same except when x = ± 1 and when x = 0. The function f(x) isn't even after all. Be Careful: When we're talking about functions, "even" and "odd" are not opposites.
In contrast to integers, which must be either even or odd, a function might not be either one. There is only a loose connection between even and odd integers and even and odd functions.
