A function 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.

 

Answers (1)
P perimeter

As we learnt in

Odd Function -

f(-x)= -f(x)

- wherein

Symmetric about origin

 

 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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