Function Theory - The Domain and Codomain(Image)

As we said earlier, a function takes a given variable or set of variables, and transforms it into another one.

Let's assume that we have a set x of numbers, say, And, the function This function acts on the elements of the set x. It takes them as an input. This is what's called the domain of a function. The input values it can work for. It's denoted as

It will then transform every x into its square, giving us the setThis set y, containing the elements after the function has transformed the domain, is what's called the image of a function. You may also encounter the name codomain. We denote it by Done!
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