A relationship (or relation) between inputs and outputs (usually referred to as x and y) can only be called a function if and only if each element of the input is paired with exactly one element of the output. That is, each x must have only one y, and no x's can be left without a y. Here, we look at input and output relations represented in what's called a "map," or "mapping." To find an inverse, swap all elements of the input and output. The set of all inputs, usually the x's, is called the domain, and the set of all outputs, usually y's, is called the range.
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