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  "body": "\n## Summary\n\nThe inverse transform of an [[integral transform|YCK709QB06]] $T$ recovers a function $f$ from its image $Tf$.\nIt exists when $T$ is one-to-one on the class of functions in use.\nOften the inverse is itself an integral transform with its own kernel.\nExamples are the Fourier inversion formula and the [[Bromwich integral|5KNAXNHRY6]] for the [[inverse Laplace transform|07WBTX1MHA]].\nA typical use of a transform is: transform the problem, solve it on the transform side, then apply the inverse transform.\n\n## Explanations\n\n### L1 human\n\nIf a transform translates functions into another language, the inverse transform translates back.\nFor the [[Fourier transform|DPVM34ADZV]], the inverse looks almost like the transform itself: only the sign in the exponential changes.\nFor the Laplace transform, the inverse needs an integral along a vertical line in the complex plane, so in practice one uses tables of [[transform pairs|ZA1HC10WM6]].\nFor example, the inverse Laplace transform of $1/(s - 2)$ is $e^{2t}$.\n",
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