Mathematics –Class XII
Unit-I:Relations and functions
Chapter-1: Relations and functions
Sub Topic: Function
Outline
(2):- (a, b) ∈ f and (a, c) ∈ f ⇒ b=c.
Let, A and be two non –empty sets. A relation f from A to B, i.e. a subset of A ×B, is called a function from A to B, if
(1):- for each a∈A there exists b ∈ B such that (a, b) ∈ f
a
b
c
d
e
1
2
3
4
5
A
B
Is it a function
a
b
c
d
e
1
2
3
4
5
A
B
Is it a function
a
b
c
d
e
1
2
3
4
5
A
B
Is it a function
a
b
c
d
e
1
2
3
4
5
A
B
function
Domain
Co-domain
a
b
c
d
e
1
2
3
4
5
A
B
function
What about Range
Range of f ={a,b,c,d,e}
1
2
3
4
5
A
B
function
What is Range here
Range of f ={b,c,d,e}
a
b
c
d
e
Range of f ={bϵB:(a, b) ∈ f }
Domain:- Let f be a function from A to B, which is written as f:A🡪B.
Then set A is domain of function
Co-domain:-
Set B is co-domain of function
Hence we concluded that
Since every element of domain have unique image ,hence it is function.
Ex:-Check whether f :A →B is defined by f (x) = x 2 ,
where A={-2,-1,0,1,2}and B={0,1,2,3,4,5} is a function ?
If yes, What is its domain and Range of f.
-2
-1
0
1
2
01
2
3
4
5
Domain of f=A={2,-1,0,1,2}
Co-domain=B={0,1,2,3,4,5}
Range of f={0,1,4}
A
B
Q-1.Check whether f :A →B is defined by f (x) = x 3,
where A={-2,-1,0,1,2}and B={0,1,4,6,8,10,12} is a
function .If yes, What is its domain and Range .
Q-2.Check whether f :N →N is defined by f (x) = x 1/2,
is a function .If yes, What is Range of f
Q-3.Check whether f :R →R is defined by f (x) = │x│, is
a function. If yes, What is Range of f
Q-4. Check whether f :R →R is defined by f (x) =
│x-3│,is a function .If yes, What is Range of f
Q-5. Check whether f :R →R is defined by f (x) = │x│+3,
is a function .If yes, What is Range of f
Assignment