Functions Part 1

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.