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To address the first situation, what we are after is a way to describe the set of images of elements in some subset of the domain. Suppose \(f:X \to Y\) is a function and that \(A \subseteq X\) is some subset of the domain (possibly all of it). We will use the notation \(f(A)\) to denote the image of \(A\) under \(f\), namely the set of elements in \(Y\) that are the image of elements from \(A\text{.}\) That is, \(f(A) = \{f(a) \in Y \st a \in A\}\text{.}\)

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