Presenter name aizaz ali

PRESENTER NAME: Aizaz Ali and Shams –ul –
Amin (students of BSCS 3rd semester at GPGDC)
PRESENTATION
PRESENTED TO: Sir Mr.Mumtaz Gohar Saib
(chairman of computer Science department
at GPGDC Landikotal)
1

PRESENTATION TOPIC IS
FUNCTIONS IN DISCREATE
MATHAMTHIC
2

PRESENTATION OF FUNCTION
In this presentation we have to only covered
function introductions and only some types and
theirs short definition.
Details we have to learn in next presentation from
shams-ul-amin
3
So let start the presentation

4AGENDA
Function and some example
Domain , co-domain ,image ,rang, preimage
What is a Function?
Types of function
Injective function and example
Bijective function and example
Exercise
References and objects

5FUNCTIO
NDefinition;- let A and B any two non empty sets then, A function from A to B is
a rule that assign to each element of set A, one and only one element of set B. or
A function is a rule|manner|correspondace|mapping define from set A to set B
that each and every element of set A has a unique image in set B.
Mathematically ,
f: Ab
where, y = f(x), x belong to A
1
2
3
A
a
b
c
B
Here in this function every
element have unique image

7
Representation of Functions
Functions are generally represented as f(x)
 Let , f(x)=x3
 It is said as f of x is equal to x cube.
 Functions can also be represented by g(),
t(),… etc.
FUNCTION

8FUNCTION
Domain;- the collection on set of the values for which a
function is define.
f(x) = 1/x
X 0
Domain of F : {a|a belong to A: (a, f(a))belong to f}
Co-domain;- set B is called co-domain
Range;- set of values used by function at per the domain
Rf ; {b|b belong to B: (a, f(b))belong to f}
F : Ab
F(x) = sinx ,,, R =m domain R: domain :[1,-1]range
Image;- b is the image of a under f
Pre-image;- a is the preimage f b under f
Function visualization

9FUNCTION
Range
preimage
Domain Co-Domain
2
A
B
Bf
1 A
image
A function f : AB

10
WHAT IS A FUNCTION?
A function relates an input to an output
It is like a machine that has an Input and an
output
Some examples of function
F(x) = X^2 (squaring) is a function
F(x) = x^3-1 is also a function

11
FUNCTION
y= f(x)
output
Name of function
Input

13
FUNCTION TOPICS
ONE TO ONE FUNCTION
 If each element in the domain of a function has a distinct image in the co- domain the
function is to be one to one function OR
 A function f from A to B is called one to one (or 1-1) if whenever f(a)=f(b) then a = b on
element of B is the image of more then one element in A
 A function is said to be injective if it is one to one
 If each and every element have a single image is also know as one to one function
1
2
a
b
A B

14
ONE TO ONE FUNCTION
Let F : RR given by f(x) = 3x+5 is one-one
1
2
3
8
11
14
X y
Each and every element have single
image this function is know as one
to one function
example

15
Many one function(subjective function)
On the other hand if there are at least two element in the domain whose
image are same the function is know as many function
 A function f from A to B is called onto it for all b in B there is an a in A such
that f(a)=b. all element in B are used
1
-1
A
2
B
Those function which have one then more
image is know as many one function
FUNCTION TOPICS

16
Example:-
Let f: RR given by f(x)=x2 is many one function
1
-1
1
x y
MANY ONE FUNCTION

17
FUNCTION EXERCISE
1
a b
1
2
A
B
4 ba
1
2
A
B
2
1
2
A
B
ba
3 ba
1
2
A
B
Is this is a function?

18
References
Learning mathematics website
Sild share website
Books on discrete mathematics
Tutorials of on discrete
mathematics

Presenter name aizaz ali

More Related Content

What's hot (18)

Similar to Presenter name aizaz ali (20)

Recently uploaded (20)

Presenter name aizaz ali