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# $If A\{x,y,z\},\:\:B=\{1,2,3\}$ 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 $f^{-1}(1)=?$

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

Since $f$ is 1-1 and only one out of the statements is true,
$f(z)\neq 2$ is true.
Remaining statements are false.
i.e.,$f(x)\neq 1$ and $f(y)=1$
$\Rightarrow \:f(y)=1,\:\:f(z)=3\:\:and\:f(x)=2$
$\Rightarrow\:f^{-1}(1)=y$

+1 vote