Kinds Of Functions
- One-to-one Function (or injective function)
A function f : is called one-one mapping if every distinct element of A has a distinct image in B.
Thus, a function f : is one-one
- Many-one Function : A function f : is many-one if two or more different elements of A have the same image in B.
Thus, f : is many-one if
- Onto or Surjective Function : The function f : 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)
- Into Function : If the function f : 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 co-domain (B)
Bijective function : A function f : is a bijective function if f is one-one as well as onto, i.e. f is injective and surjective both.