InterviewSolution
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InterviewSolution
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Let `A ={1,2,3 } " and let " f: A to A ` defined by `f ={(1,2),(2,3) , (3,1)}` Find `f^(-1)` if it exists . |
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Answer» We have `f(1)=2 , f(2) =3 " and " f(3) =1` Don `(f ) ={1,2,3} = A and range " ( f) ={1,2,3}=A` Clearly different elements in A have different images . `:.` f is one -one . Range (f ) `=A rArr f ` is onto. Thus f is one-one onto and therefore invertible . Now `f(1) =2 , f(2) =3 " and " f(3) =1` `rArr f^(-1) (2)=1 , f^(-1) (3) =2 " and " f^(-1) (1) =3` Hence `f^(-1) ={(2,1) , (3,2) ,(1,3)}` |
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