UPSC NDA Math Model Paper 10

Given: f : N → N and is defined as f (x) = x + 1
One - One:
Let f(x1)=f(x2)
⇒x1+1=x2+1
⇒x1=x2
Hence, the given function f is one - one.
Onto:
Let y = f(x) = x + 1
⇒ x = y -1
But If y = 1 ∈ N then x = 0 ∉ N.
Hence, all the elements of co - domain i.e N does not has a pre - image in the domain i.e N.
Hence, the given function is not onto.