In mathematics, particularly in the context of set theory and functions, a restriction refers to the process of limiting the domain or the codomain of a function or relation.
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For a function and a subset , its restriction keeps the same values but allows only inputs in . Restricting the domain of a function can remove collisions and permit an inverse function, as the nonnegative quadratic function example shows. This changes the allowed inputs; it is different from keeping the inputs and changing the codomain.