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  "body": "\n## Definition\n\nLet $f \\colon A \\to B$ be a [[bijective function|0SNQEF7Z53]].\nThe inverse function of $f$ is the function $f^{-1} \\colon B \\to A$ such that, for each $b \\in B$, $f^{-1}(b)$ is the unique $a \\in A$ with $f(a) = b$.\n\n## Remarks\n\nThen $f^{-1} \\circ f = \\mathrm{id}_A$ and $f \\circ f^{-1} = \\mathrm{id}_B$. See [[bijective iff it has a two-sided inverse|01VG2A0BHW]].\nThe inverse $f^{-1}$ is a bijection, and its inverse is $f$.\nExample: the inverse of $x \\mapsto 2x + 1$ on $\\mathbb{R}$ is $y \\mapsto (y - 1)/2$.\nDo not confuse $f^{-1}(b)$ with the [[preimage|0FGCFY1AZX]] $f^{-1}(\\{b\\})$, which exists for every function.\n\n## Explanations\n\n### L1 human\n\nTo find the inverse of $y = 2x + 1$, solve for $x$: $x = (y - 1)/2$.\nThe inverse runs the function backwards.\nIts graph is the graph of $f$ reflected in the line $y = x$.\n",
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