Computable Injective Function

Algebra Level 3

Let f be a One-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 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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