On-To function

2. OnTo Function:-

If each and every element of the range has at least one preimage in the domain.

What it means is: let us say there are 4 elements in Range and they all are mapped to at least one element in Domain.

So for this condition, there must be at least 4 elements in Domain. Why not less than 4?

Because we already know that each element of the domain can be mapped with at most one element of Range. If there are less than 4 elements then one element of Range is left unmapped. That's why we need at least 4 elements in Domain.


3. Bijection Function:-

A function is bijection iff

  • The function is one-one.
  • The function is onto.

If A and  B are finite set then Bijection from A to B is possible only iff 

|A| =|B| =n

Total no.of Bijection Possible is:  n!


4.Inverse function:-

let f: A\rightarrow B and  a function f^{_{-1}}: B\rightarrow A  is called the inverse of f.


Necessary Condition for Inverse function:-

  • The original function should be one-one.
  • The original function should be onto.
  • Inverse exist only for Bijective Function.