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  "body": "\n## Definition\n\nLet $f \\colon A \\to B$ be a [[function|0XHDTE5YMZ]] and let $S$ be a [[subset|0FE8Q5S42Y]] of $A$.\nThe image of $S$ under $f$ is the set\n$$f(S) = \\{f(s) \\mid s \\in S\\} = \\{b \\in B \\mid \\exists s \\in S, \\, f(s) = b\\}.$$\n\n## Remarks\n\nAnother notation is $f[S]$. It avoids a confusion with $f(a)$ for an element $a$.\nThe image $f(A)$ of the whole domain is the [[range|0E9GTAV478]] of $f$.\nExample: for $f(x) = x^2$ on $\\mathbb{R}$, $f([-1, 2]) = [0, 4]$.\nThe image of a union is the union of the images, but the image of an intersection can be smaller. See [[image of an intersection|0RX7DDBYCK]].\n\n## Explanations\n\n### L1 human\n\nTo compute $f(S)$, apply $f$ to each element of $S$ and collect the results.\nFor $f(x) = x + 1$ and $S = \\{1, 2, 3\\}$, the image is $\\{2, 3, 4\\}$.\n",
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