Restriction (mathematics, $f{|}_A:A\to Y$)

For a function $f:X\to Y$ and a subset $A\subseteq X$, its restriction $f{|}_A$ keeps the same values but allows only inputs in $A$. 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.