Show that an affine function maps affine sets to affine sets, and vice versa. That is, if

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Show that an affine function maps affine sets to affine sets, and vice versa. That is, if S is an affine subset of X, then f (S) is an affine subset of Y; if T is an affine subset of Y, then f-1 (T) is an affine subset of X.
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