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  "body": "\n## Definition\n\nLet $f \\colon A \\to B$ and $g \\colon B \\to C$ be [[functions|0XHDTE5YMZ]].\nThe composition of $g$ and $f$ is the function $g \\circ f \\colon A \\to C$ with\n$$(g \\circ f)(a) = g(f(a))$$\nfor each $a \\in A$.\n\n## Remarks\n\nRead $g \\circ f$ as \"$g$ after $f$\": $f$ acts first.\nIn general $g \\circ f \\neq f \\circ g$. For $f(x) = x + 1$ and $g(x) = 2x$ on $\\mathbb{R}$, $(g \\circ f)(x) = 2x + 2$ and $(f \\circ g)(x) = 2x + 1$.\nComposition is associative. See [[associativity of composition|0J6AKYZQT8]].\n\n## Explanations\n\n### L1 human\n\nComposition chains two machines: the output of $f$ goes into $g$.\nFor $g \\circ f$ to make sense, the values of $f$ must lie in the domain of $g$.\n",
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