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Kinds Of Functions

  1. One-to-one Function (or injective function)
    A function f 736.png is called one-one mapping if every distinct element of A has a distinct image in B.
    Thus, a function f 741.png is one-one
  2. Many-one Function : A function f : 746.png is many-one if two or more different elements of A have the same image in B.
    Thus, f : 751.png is many-one if
  3. Onto or Surjective Function : The function f : 756.png is said to be an onto function if every element of B is image of at least one element of A.
    For a surjective function f,
    Range of f = co-domain (B)
  4. Into Function : If the function f 761.png is such that there is at least one element of B which is not the image of any element of A, then f is called an into function.
    For an into function f.
    Range of f 766.png co-domain (B)


Bijective function : 
A function f : 776.png is a bijective function if f is one-one as well as onto, i.e. f is injective and surjective both.


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