1function definition
function from A to B is rule which assigns every elements of set A to unique elements of set B
2onto functions
|A| ≥ |B| , IF B IS CODOMAIN OF A ( injective function)
3one one function
A| ≥ |B| , IF A IS CODOMAIN OF B ( surjective function)
4Bijective function
IF function is injective and surjective both and |A| = |B|
5can we have a bijective function from Z to R
No , | Z | <|R|
6Equality of two function
IF F1 AND F2 FUNCTION IS , F1=F2
8fog is one one then g must be one one
right
9if g is one one then fog is one one
No
10fog is onto then f must be onto
right
11condition for inverse function
must be onto and one one / ( bijective function)
12graph of identity function
function A tens to B , f(a)=a , for all age belongs to A , graph like y=x