Give an example of a function

Which is neither one – one nor onto.

TIP: – One – One Function: – A function is said to be a one – one functions or an injection if different elements of A have different images in B.

So, is One – One function

⇔ a≠b

⇒ f(a)≠f(b) for all

⇔ f(a) = f(b)

⇒ a = b for all

Onto Function: – A function is said to be a onto function or surjection if every element of A i.e, if f(A) = B or range of f is the co – domain of f.

So, is Surjection iff for each , there exists such that f(a) = b

Now, Let, given by f(x) = 5

As we know

A constant function is neither one – one nor onto.

So, here f(x) = 5 is constant function

Therefore

given by f(x) = 5 is neither one – one nor onto function.