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I'm looking to find the name and the formal definition of functions which their output has a restricted domain like this:

Suppose the function has two inputs in a domain of [1-100]. The result of this function on these inputs is always in a domain of [1-100] as well, e.g, Maximum function. But a function like Sum of two integers is not like this, as its output would break the borderlines.

Do you know what this kind of functions has been called? And what is the formal definition of them?

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