# 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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