Computable Injective Function

Algebra Level 2

Let ff be a one-to-one (Injective) function with domain Df={x,y,z}D_{f} = \{x,y,z\} and range {1,2,3}.\{1,2,3\}. It is given that only one of the following 33 statement is true and the remaining statements are false:

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

Find f1(1). f^{-1} (1).

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