Computable Injective Function

Algebra Level 2

Let \(f\) be a one-to-one (Injective) function with domain \(D_{f} = \{x,y,z\} \) and range \(\{1,2,3\}.\) It is given that only one of the following \(3\) statement is true and the remaining statements are false:

\[ \begin{eqnarray} f(x) &=& 1 \\ f(y) & \neq & 1 \\ f(z)& \neq & 2. \\ \end{eqnarray} \]

Find \( f^{-1} (1). \)

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