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Let a function \mathrm{f: N \rightarrow N} be defined by
\mathrm{f(n)=\left[\begin{array}{ll} 2 n, & n=2,4,6,8, \ldots \\ n-1, & n=3,7,11,15, \ldots \\ \frac{n+1}{2}, & n=1,5,9,13, \ldots . \end{array}\right.}    then ,\mathrm{f} is

Option: 1

one-one but not onto


Option: 2

onto but not one-one


Option: 3

neither one-one nor onto


Option: 4

 one-one and onto


Answers (1)

best_answer
\mathrm{n} 1 2 3 4 5 6 7 8 9
\mathrm{f\left ( n \right )} 1   4 2 8 3 12 6 16 5

As can be seen , All the odd numbers are  given by the third sequence

All the \mathrm{4n} type numbers are given by the first sequence
All the \mathrm{4n{+2}} type numbers are given by the second sequence

So the function is one-one and onto.

Option (D)

Posted by

Ritika Kankaria

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