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Consider the function \(f:\{1,2,3,4,5,6\} \to \{a,b,c,d\}\) given by

\begin{equation*} f = \begin{pmatrix}1 \amp 2 \amp 3 \amp 4 \amp 5 \amp 6 \\ a \amp a \amp b \amp b \amp b \amp c\end{pmatrix}\text{.} \end{equation*}

Find \(f(\{1,2,3\})\text{,}\) \(f\inv(\{a,b\})\text{,}\) and \(f\inv(d)\text{.}\)

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