If function f such that A→B is such that Range f ⊂ B that is Range

f ≠ B then f is said to be a function from A into B

figure show that

f is clearly a function. But Ran f ≠ B

therefore, f is a functions for, A to B

(2) Onto function or(Surjective function):

if a function ƒ: A →B is such that Ran ƒ = B that is every element of B is the image of some element of A then ƒ is called an Onto function

Types of function example figure

(3) INJECTIVE FUNCTION :

if a function ƒ from A to B is such that the second element of no two of its ordered pair are equal, then it is called an injective (1,-1 and into) function

From figure:

(4) (1, -1) and onto function (bijective function)

If ƒ is a function from A onto B such that the second element of no two of its ordered pairs are the same. Then f is said to be (1,-1) function from A to B

such the function is also called a (1,-1) correspondence between A and B. It is also called a bijective function.