Function


   
 
Types of Functions (Mapping)
(1) One-one function
 
(2) Many-one function
 
(3) Onto function
 
(4) Into function
 
Let the relation be from set A to set B.
 
1. One-one function
 
There is one-one correspondence between the elements of the set A and the set B.
 
 
2. Many-one function
 
There is many-one correspondence between the elements of the set A and the set B.
 
 
3. Onto function
 
Every element of the set B has at least one pre-image.
 
 
 
In above fig.(i), the function is one-one and onto, while in fig.(ii) the function is many-one and onto.
 
4. Into function
 
There is at least one element of B which has no pre-image.
 
 
 
In above fig.(i) the function is one-one and into, while in fig.(ii) the function is many-one and into.
 
 
For types of functions, the four arrow diagrams given for one-one and many-one are repeated for ONTO and INTO functions because each function is always one-one onto or one-one into; many-one onto or many-one into.
 
  
     
   
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