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  "body": "\n## Definition\n\nLet $f \\colon A \\to B$ be a [[function|0XHDTE5YMZ]] and let $S$ be a [[subset|0FE8Q5S42Y]] of $A$.\nThe restriction of $f$ to $S$ is the function $f|_S \\colon S \\to B$ with $f|_S(s) = f(s)$ for each $s \\in S$.\n\n## Remarks\n\nThe graph of $f|_S$ is $\\{(s, f(s)) \\mid s \\in S\\}$, a subset of the graph of $f$.\nThe function $f$ is an extension of $f|_S$.\nExample: $x \\mapsto x^2$ on $\\mathbb{R}$ is not [[injective|0PVG1CRAJN]], but its restriction to $[0, \\infty)$ is injective.\n\n## Explanations\n\n### L1 human\n\nTo restrict a function, you keep its rule and allow fewer inputs.\nRestrictions often make a function injective, so that it has an inverse on a smaller domain.\n",
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