The document defines functions and different types of functions. It begins by defining a function as a relation where each element in the domain is paired with exactly one element in the range. It then discusses function notation using f(x) = y. The document presents examples of one-to-one, onto, and bijective functions. It also defines the inverse of a function as the relation formed by switching the domain and range.

2. Submitted to:
Falguni Roy
Lecturer,
Institute of Information Technology (IIT)
NSTU

3. Emran Hossain
Roll:ASH1825002M
Muin Uddin
Roll:ASH1825012M
Presented by:
Anwar Kabir
Roll:ASH1825038M
Azad Hossain
Roll:ASH1825014M

4. Anwar Kabir
Roll:ASH1825038M
Azad Hossain
Roll:ASH1825014M

5. Slide Introduction
• Definition of a function
• Representation of a function
• Special types of function

6. DEFINATION
f(x)x Y
• A function is a relation in which each element of the domain is paired with
exactly one element of the range.
• Another way of saying it is that there is one and only one output (y) with
each input (x). X is called Domain & Y is called Codomain of function ‘f ’.

7. Function Notation
y = f(x)
Input
Input
Name of
function
Output

8. 1
2
3
D
B
C
A
Domain Codomain
The above diagram represents a function with domain {1,2,3} ,codomain{A,B,C,D} & set of
ordered pairs {(1,D),(2,C),(3,C)}.The image is {C,D}.
Domain & Codomain of a function

9. Types of function
• Injective / One-to-one function
• Surjective / Onto function
• Bijective / One-to-one correspondent
• Inverse function

10. Injective / One-to-one function

11. Example of one-to-one function

12. Model of one-to-one function
Figure:1 Figure:2

13. Surjective / Onto function

14. Example of onto function
Figure:1 Figure:2

15. Bijective function

16. Example of bijective
Figure:1 Figure:2

17. Inverse of a function

18. 1
3
4
4
6
0
1
3
4
4
6
0
Domain Range RangeDomain
Domain and Range are switched
Functions & it’s Inverse
(1,4)
(3,6)
(4,0)
(4,1)
(6,3)
(0,4)