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Edited By Ramraj Saini | Updated on Mar 22, 2022 04:40 PM IST

Class 11 Math chapter 2 notes are regarding Relations and Functions. In chapter 2 we will be going through the functions and their relations concepts in Relations and Functions Class 11 notes. This Class 11 Maths chapter 2 notes contains the following topics: Cartesian product, relations, functions, different types of functions, Algebra of a real function, multiplication of two real functions, quotient function.

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NCERT Class 11 Math chapter 2 notes also contain important formulas. NCERT Class 11 Math chapter 2 contains systematic explanations of topics using examples and exercises. NCERT Notes for Class 11 Math chapter 2 include FAQ’s or frequently asked questions about the chapter. In CBSE Class 11 Maths chapter 2 notes topics are explained step by step. These concepts can also be downloaded from Class 11 Maths chapter 2 notes pdf download, Class 11 notes Relations and functions, Class 11 Relations and functions notes pdf download.

**Also, students can refer,**

- NCERT Solutions for Class 11 Maths Chapter 2 Relations And Functions
- NCERT Exemplar Class 11 Maths Chapter 2 Relations And Functions

**Ordered Pair:** two elements in an order separated by common.

Representation: (a,b)

NOTE: 2 ordered pairs (a,b) and (c,d) are said to be equal if (a=c) and (b=d)

**Cartesian Product: **If sets A, B have an ordered pair of (a,b) where a A and b B, is called cartesian product.

Denoted by: AXB

Set builder form: AXB ={(a,b) : a ∈A and b∈ B}

**NOTE: **

If A=∅ , B= ∅then cartesian product AXB=∅.

It doesn’t satisfy commutative law: (A, B)≠(B, A)

If anyone among the two sets is an infinite set then the whole product becomes infinite.

A=infinite, B=finite then AXB and BXA are also infinite.

If n(A)=m (m=number of elements in A), n(B)=n then the number of elements in the cartesian product is mn.

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Download EBookEg: n(A) = 3 and n(B)=2 then n(AXB) = 6.

**Relations: **

A group of ordered pairs containing one element from each set is called the relation between two sets. Suppose A, B are both non-empty sets, then the relation is a subset of cartesian products of (AXB).

A subset is a relation between the first and second elements of ordered pairs in A × B.

The set of first elements in relations is called the domain and the next element is called images or of range R.

Set builder form: R={(a,b): (a,b)∈R}

**Representation Of Relation:**

**Note:**

- The range can be represented in set-builder, roaster form, and also using arrow marks with brackets.
- If n(A)=m (m=number of elements in A), n(B)=n, and cartesian product=mn then a number of relations can be found by using

**Inverse Relation:**

Sets A, B are both non-empty sets with R being the relation and the inverse of the relation is called inverse relation from B to A.

A relation F from A to B is called to be a function if every element in set A of a function has only one image in set B of a function.

Function denoted as f: A→B is said to be a real-valued function if B is a subset of R . If A, B are subsets of R, in such conditions we can call f is called a real function.

**Identity function:**

A function is said to be an identity function if a function f: R→R when f(x)=x for each x belongs to R satisfies.

Consider the graph of an identity function f(x)=x:

Domain= R

Range = C

**Constant Function :**

A function is said to be a constant function, if a function f: R R when f(x)=C for each C belonging to R satisfies.

Consider the graph of a constant function:

Domain= R

Range = C

**Polynomial Function:**

A function is said to be a Polynomial function, if a function f: RR when for each x belonging to R satisfies.

**Rational Functions:**

The functions that belong to Real functions, and are represented as f(x)/g(x) where f(x) and g(x) ≠0 are polynomial functions that are represented using x and they belong to R.

**Modulus Function:**

Real function f: R → R is said to be a modulus function if

**Signum Function:**

Real function f: R → R is said to be Signum function if f(x) = lxl / x where x≠0 and when x=0 we get

Domain= R

Range={-1,0,1}

**Greatest Integer Function:**

Real function f: R → R is said to be the greatest integer function if f(x)=[x] where x belongs to R and values of x are the greatest integer or less than or equal to x.

**Fractional Function:**

Real function f : R → R is said to be Fractional Function function if f(x)={x} where x belongs to R.

f(x) = {x} = x – [x]

Domain: R

Range : [0,1)

**Addition Of Two Algebraic Functions:**

If f : X → R , g : X → R are real functions, then we represent: (f + g) : X → R as (f + g) (x) = f (x) +g(x) where x belongs to X.

**Subtraction Of Real Functions:**

If f : X → R and g : X → R are real functions, then we represent : (f – g) : X → R as (f – g) (x) = f (x) – g(x) where x belongs to X.

**Multiplication Of Scalar:**

If f : X → R is real functions, K is any scalar

product of Kf is defined by : (Kf)(x) = Kf(x)

**Multiplication Of Two Real Functions:**

If f : X → R and g : X → R are real functions,

product of the two functions is defined by: (fg) x = f(x) . g(x)

**The Quotient Of Two Real Functions:**

if f and g are two real functions, then the

The quotient of f by g is given by fg from XR.

(f/g)(x) = f(x)/g(x) where g(x)≠0

With this topic we conclude NCERT Class 11 chapter 2 notes.

The link for the NCERT textbook pdf is given below:

URL: ncert.nic.in/pdf/publication/exemplarproblem/classXI/mathematics/keep202.pdf

NCERT Class 11 Maths chapter 2 notes will be very much helpful for students to score maximum marks in their 11 board exams. In Relations and Functions Class 11 chapter 2 notes we have discussed many topics: Cartesian product, relations, functions, different types of functions, Algebra of a real function, multiplication of two real functions, quotient function. NCERT Class 11 Maths chapter 2 covers important topics of Class 11 CBSE Maths Syllabus.

The CBSE Class 11 Maths chapter 2 will help to understand the formulas, statements, rules in detail. This pdf also contains previous year questions and NCERT textbook pdf. The next part contains FAQ’s or frequently asked questions along with topic-wise explanations. These topics can als be downloaded from Class 11 chapter 2 Relations and Functions pdf download.

**NCERT Class 11 Notes Chapter Wise.**

NCERT Class 11 Maths Chapter 2 Notes |

- NCERT Exemplar Class 11 Solutions
- NCERT Exemplar Class 11 Maths
- NCERT Exemplar Class 11 Physics
- NCERT Exemplar Class 11 Chemistry
- NCERT Exemplar Class 11x Biology

- NCERT Solutions for Class 11 Mathematics
- NCERT Solutions for Class 11 Chemistry
- NCERT Solutions for Class 11 Physics

1. What does pre-image mean in Relations and Functions Class 11 notes?

If f(x)=y with a function f mapping from x to y the y is an image of x and x is called the preimage of y.

2. What does codomain mean in NCERT Class 11 Math chapter 2 notes/ Relations and Functions Class 11 notes?

Codomain is a set of all possible values of the given function that come out as a result.

3. What are real numbers according to ncert notes for class 11 maths chapter 2/ NCERT Class 11 Maths chapter 2 notes? Under which category 0 is included?

Real numbers are all those which are positive, negative, and including zero. So zero is also a real number.

4. What is the importance of Class 11 notes Relations and functions?

It is a very important concept in algebra. It is used to determine one number using another number that is possible by functions and mapping.

5. What are real-life applications of Relations and Functions Class 11 notes?

Relations and functions give us a link between two quantities. Here output depends on the input.

Eg: Marriage where it depends on one other as a link to continue the relationship.

Similarly father and son, mother and son, etc.

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