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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 :
$R\to R$
by y = f (x), x
$\in $
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
$f:R\to R$
by y = f (x) = c, x
$\in $
R
where c is a constant and each x
$\in $
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.
$f:\mathit{N}\mathbf{\to}\mathit{N}byf\left(x\right)=2x+1.U\mathrm{sin}gthisdefinition,completethetablegivenbelow:-$
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
$A\times B$
. If n(A) = p and n(B) = q, then
$n\left(A\times B\right)=pq$
and the total number of relations is
${2}^{pq}$
.
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
$\subseteq $
codomain.
Answer
1
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Q. What is Rational function?

Example .13.Define the function f : $R\to R$ by y = f (x), x $\in $ R. Complete the table given below by using this definition. What is the domain and range of the function? Draw the graph of f.Constant function:Define the function $f:R\to R$ by y = f (x) = c, x $\in $Rwhere c is a constant and each x $\in $R. Here domain of f isRand its range is {c}.Let N be a set of natural numbers. Define a real valued function.

$f:\mathit{N}\mathbf{\to}\mathit{N}byf\left(x\right)=2x+1.U\mathrm{sin}gthisdefinition,completethetablegivenbelow:-$

Definition 6A 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.

Explain noteNote:The total number of relations that can be defined from a set A to a set B is the number of possible subsets of $A\times B$. If n(A) = p and n(B) = q, then $n\left(A\times B\right)=pq$ and the total number of relations is ${2}^{pq}$.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 2A 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 3The 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 4The 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 $\subseteq $ codomain.