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## Main Question or Discussion Point

**"Dual-output" Function?**

This isn't homework: I am experimenting with factorization.

Does anyone know of a function f(x) which for some value of x returns one value for f(x), but for every other value of x returns some other value?

Example: I'm trying to find a function f(x), where

x = 0, f(x) = 1

x != 0, f(x) = 0

My function is only dealing with non-negative integers, if that helps.

I've already derived a function that does this, but it uses absolute values, which is a nuisance.

Anyone know of anything like this?

For reference, here is my formula:

[tex]f(x) =\frac{1-\frac{\left|2x-1\right|}{2x-1}}{2} = \frac{\left|4x-2\right| - 4x-2}{8x-4}[/tex]

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