$If A\{x,y,z\},\:\:B=\{1,2,3\}$ and $f:A\rightarrow B\:\:is\:1-1\:$function. Also one out of the following statements, $f(z)\neq 2,\:\:f(x)=1\:\:and\:\:f(y)\neq 1$ is true. then $f^{-1}(1)=?$

Question

$(A) \; x \\(B)\; y \\(C)\; z \\(D)\; cannot\;be\;determined$