# A function $\dpi{100} f$  from the set of natural numbers to integers defined by is Option 1) onto but not one­-one Option 2) one­-one and onto both Option 3) neither one-­one nor onto Option 4) one­-one but not onto.

P perimeter

As we learnt in

Odd Function -

$f(-x)= -f(x)$

- wherein

$f(x)=\left\{\begin{matrix} \frac{n-1}{2} & when\ n\ is\ odd\\ -\frac{n}{2}& when\ n\ is\ even \end{matrix}\right.$

For n odd: $\frac{n-1}{2}$ will be different values

For n even: $-\frac{n}{2}$  will be different values

So then is one one and $R\leq\ coordinate$

So that it is onto both are even

Correct option is 2.

Option 1)

onto but not one­-one

This is an incorrect option.

Option 2)

one­-one and onto both

This is the correct option.

Option 3)

neither one-­one nor onto

This is an incorrect option.

Option 4)

one­-one but not onto.

This is an incorrect option.

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