# 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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