UPSC NDA Math Model Paper 3

Let's check the given function f(n) = 3n + 4, ∀ n ∈ N for one-to-one and onto:
Injective: Let's say 3n+4=k⇒n=

k−4

3

It means that for every value of k, we will get only a single value of n, therefore the function is injective.
Surjective: Since n=

k−4

3

, not all values of k will give n ∈ N. So, the function is not surjective.
Bijective: Since the function is injective but not surjective, it is not bijective.
So, the function f is only injective.