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The function f(x) is even, right? Nope. If we used x instead of the specific number 1 we would find
f(x) = x3 – x f(-x) = -x3 + 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.