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  "body": "\n## Statement\n\nLet $D, E \\subseteq \\mathbb{R}$, let $f \\colon D \\to \\mathbb{R}$ be a function with $f(D) \\subseteq E$, and let $g \\colon E \\to \\mathbb{R}$.\nIf $f$ is continuous at $a \\in D$ and $g$ is continuous at $f(a)$, then $g \\circ f$ is continuous at $a$.\nIn particular, if $f$ and $g$ are [[continuous|0P27W9RW0G]], then $g \\circ f$ is continuous.\n\n## Remarks\n\nGiven $\\varepsilon \u003e 0$, choose $\\eta \u003e 0$ for $g$ at $f(a)$, and then $\\delta \u003e 0$ for $f$ at $a$ and the tolerance $\\eta$. See the [[epsilon-delta form|0W8YHHGCJG]].\nFor example, $x \\mapsto \\sin(x^2)$ is continuous.\nMathlib states it for topological spaces, as `Continuous.comp`.\n\n## Explanations\n\n### L1 human\n\nA small change of $x$ gives a small change of $f(x)$.\nThis in turn gives a small change of $g(f(x))$.\n",
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