NCERT Solutions
Board Paper Solutions
Ask & Answer
School Talk
Login
GET APP
Login
Create Account
Popular
Latest
अर्कज
Subject: Maths
, asked on 4/5/18
Explain Signum function
Answer
1
अर्कज
Subject: Maths
, asked on 4/5/18
Q. What is Rational function?
Answer
1
अर्कज
Subject: Maths
, asked on 4/5/18
Explain Modulus function
Answer
1
अर्कज
Subject: Maths
, asked on 4/5/18
Example .13.
Define the function f :
R
→
R
by y = f (x), x
∈
R. Complete the table given below by using this definition. What is the domain and range of the function? Draw the graph of f.
Answer
1
अर्कज
Subject: Maths
, asked on 4/5/18
Polynomial function
Answer
1
अर्कज
Subject: Maths
, asked on 4/5/18
Q.(ii).
Constant function:
Define the function
f
:
R
→
R
by y = f (x) = c, x
∈
R
where c is a constant and each x
∈
R
. Here domain of f is
R
and its range is {c}.
Answer
2
अर्कज
Subject: Maths
, asked on 4/5/18
Explain Identity functions
Answer
1
अर्कज
Subject: Maths
, asked on 4/5/18
Example 12
Let N be a set of natural numbers. Define a real valued function.
f
:
N
→
N
b
y
f
(
x
)
=
2
x
+
1
.
U
sin
g
t
h
i
s
d
e
f
i
n
i
t
i
o
n
,
c
o
m
p
l
e
t
e
t
h
e
t
a
b
l
e
g
i
v
e
n
b
e
l
o
w
:
-
x
1
2
3
4
5
6
7
y
f(1) = ......
f(2) = ......
f(3) = ......
f(4) = ......
f(5) = ......
f(6) = ......
f(7) = ......
Answer
1
अर्कज
Subject: Maths
, asked on 4/5/18
Definition 6:
Definition 6
A function which has either R or one of its subsets as its range is called a real valued function. Further, if its domain is also either R or a subset of R, it is called a real function.
Answer
1
अर्कज
Subject: Maths
, asked on 4/5/18
Explain functions and definition 5: A relation f from a set A to a set B is said to be a function if every
element of set A has one and only one image in set B.
Answer
2
अर्कज
Subject: Maths
, asked on 4/5/18
Explain Remarks
A relation R from A to A is also stated as a relation on A.
Answer
1
अर्कज
Subject: Maths
, asked on 4/5/18
Q).
Explain note
Note:
The total number of relations that can be defined from a set A to a set B is the number of possible subsets of
A
×
B
. If n(A) = p and n(B) = q, then
n
A
×
B
=
p
q
and the total number of relations is
2
p
q
.
Answer
1
अर्कज
Subject: Maths
, asked on 4/5/18
Example 7:
Example 7:-
Let A=, {1,2,3,4,5,6}. Define a relation R from A to A by R={(x,y):y=x+1}
(i) Depict this relation using an arrow diagram.
(ii) Write down the domain, codomain the range of R.
Answer
1
अर्कज
Subject: Maths
, asked on 4/5/18
Explain Remarks
Remarks
(i) A relation may be represented algebraically either by the Roster method or by the Set-builder method.
(i) An arrow diagram is a visual representation of a relation.
Answer
1
अर्कज
Subject: Maths
, asked on 4/5/18
Meaning of definition 2,3,4
Definition 2
A relation R from a non-empty set A to a non-empty set B is a subset of the cartesian product AxB. The subset is derived by describing a relationship between the first element and the second element of the ordered pairs in A X B. The second element is called the image of the first element.
Definition 3
The set of all first elements of the ordered pairs in a relation R from a set A to set B is called the domain of the relation R.
Definition 4
The set of all second elements in a relation R from a set A to a set B is called the range of the relation R. The whole set B is called the codomain of the relation R. Note that range
⊆
codomain.
Answer
1
Prev
6
7
8
9
10
Next
What are you looking for?
Q. What is Rational function?
Let N be a set of natural numbers. Define a real valued function.
Definition 6 A function which has either R or one of its subsets as its range is called a real valued function. Further, if its domain is also either R or a subset of R, it is called a real function.
element of set A has one and only one image in set B.
A relation R from A to A is also stated as a relation on A.
Note: The total number of relations that can be defined from a set A to a set B is the number of possible subsets of . If n(A) = p and n(B) = q, then and the total number of relations is .
Example 7:- Let A=, {1,2,3,4,5,6}. Define a relation R from A to A by R={(x,y):y=x+1}
(i) Depict this relation using an arrow diagram.
(ii) Write down the domain, codomain the range of R.
Remarks (i) A relation may be represented algebraically either by the Roster method or by the Set-builder method.
(i) An arrow diagram is a visual representation of a relation.
Definition 2 A relation R from a non-empty set A to a non-empty set B is a subset of the cartesian product AxB. The subset is derived by describing a relationship between the first element and the second element of the ordered pairs in A X B. The second element is called the image of the first element.
Definition 3 The set of all first elements of the ordered pairs in a relation R from a set A to set B is called the domain of the relation R.
Definition 4 The set of all second elements in a relation R from a set A to a set B is called the range of the relation R. The whole set B is called the codomain of the relation R. Note that range codomain.