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text: 'The image $\\operatorname{im}(f)$ of a [3jy function] $f : X \\to Y$ is the set of all possible outputs of $f$, which is a subset of $Y$. Using [3lj set builder notation], $\\operatorname{im}(f) = \\{f(x) \\mid x \\in X\\}.$\n\nVisualizing a function as a map that takes every point in an input set to one point in an output set, the image is the set of all places where $f$-arrows land (pictured as the yellow subset of $Y$ in the image below).\n\n\n\nThe image of a function is not to be confused with the [3lg codomain], which is the _type_ of output that the function produces. For example, consider the [43x Ackermann function], which is a very fast-growing (and difficult to compute) function. When someone asks what sort of thing the Ackermann function produces, the natural answer is not "something from a sparse and hard-to-calculate set of numbers that I can't tell you off the top of my head"; the natural answer is "it outputs a number." In this case, the codomain is "number", while the image is the sparse and hard-to-calculate subset of numbers. For more on this distinction, see the page on [3lv codomain vs image].',
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