Let f  be injective map with domain {x,y,z}  and range {1,2,4}  such that exactly one of the following statement is correct and the remaining are false f(x)=1,f(y)≠1,f(z)≠2  then f−1(1)  is equal to

Case – I : If 1 true 2 false and 3 false f(x)=1,f(y)=1,f(z)=2 ⇒f is not 1−1 Case – II : If (1) false (2) true and (3) falsef(x)≠1,f(y)≠1,f(z)=2 ⇒f is not 1−1 Case – III : If (1) and (2) false and (3) true ⇒f(x)≠1,f(y)≠1,f(z)≠2 ⇒f(x)=2,f(y)=2,f(z)=4⇒f−1(1)=y&f−1(4)=z