`f : N to N : f (x) =x^(2) + x+ 1 ` isA. one-one and ontoB. one - one – InterviewSolution

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1.	`f : N to N : f (x) =x^(2) + x+ 1 ` isA. one-one and ontoB. one - one and intoC. many -one and ontoD. many -one and into
Answer» Correct Answer - B `f(x_(1)) =f(x_(2)) rArr x_(1)^(2) +x_(1) +1=x_(2)^(2) +x_(2)+1` `rArr (x_(1)^(2)-x_(2)^(2)) +(x_(1)-x_(2))=0rArr (x_(1)_x_(2))(x_(1) +x_(2)+1)=0` `rArr x_(1)-x_(2) =0rArr x_(1)=x_(2)`. `:. ` f is one-one `f(x) =1 rArr x^(2) +x+1 =1 rArr x(x +1) =0 rArr x=0 " or " x=-1` And none of 0 and -1 is in gt So f in into .

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