We have f:N→I If x and y are two even natural numbers, then f(x)=f(y)⇒
−x
2
=
−y
2
⇒x=y Again if x and y are two odd natural numbers then f(x)=f(y)⇒
x−1
2
=
y−1
2
⇒x=y ∴f is onto. Also each negative integer is an image of even natural number and each positive integer is an image of odd natural number. ∴f is onto. Hence f is one one and onto both.