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  "body": "\n## Summary\n\nA transform pair is a function $f$ together with its image $F = Tf$ under an [[integral transform|YCK709QB06]] $T$.\nIt is often written $f \\leftrightarrow F$ or $f(t) \\leftrightarrow F(s)$.\nTables of transform pairs are the main working tool of the [[Laplace transform|0V49JEZW06]] and the [[Fourier transform|DPVM34ADZV]].\nThey let one go back from $F$ to $f$ without computing an [[inverse transform|GC96MQC0PP]].\n\n## Explanations\n\n### L1 human\n\nA transform pair is one line of a dictionary between two languages.\nOn the left is a function of time, on the right is its transform.\nFor the Laplace transform, $e^{at} \\leftrightarrow 1/(s - a)$ is such a line.\nWhen a calculation ends with $1/(s - a)$, one looks up the line and reads off $e^{at}$.\nThis only works because the transform is one-to-one on the functions in the table.\n",
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