Let `A = R -{3} " and " B =R -{1}. " Then " f : A to B : f (x) = ((x-2 – InterviewSolution

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1.	Let `A = R -{3} " and " B =R -{1}. " Then " f : A to B : f (x) = ((x-2))/((x-3))` isA. one-one and intoB. one -one and ontoC. many-one and intoD. many -one and onto
Answer» Correct Answer - B `f(x_(1)) =f(x_(2)) rArr .((x_(1) -2))/((x_(1)-3)) =((x_(2)-2))/((x_(3)-3)) rArr x_(1)=x_(2).`So f is one-one Let `(x-2)/(x-3) =y.` then `x=(3y-2)/(y-1)` Clearly `y ne 1` and `x ne 3` ` :. `f(x) =y and so f is onto

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