VMC VIQ Scholarship Test
ApplyRegister for Vidyamandir Intellect Quest. Get Scholarship and Cash Rewards.
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.
JEE Main Scholarship Test Kit (Class 11): Narayana | Physics Wallah | Aakash | Unacademy
Suggested: JEE Main: high scoring chapters | Past 10 year's papers
Scholarship Test: Vidyamandir Intellect Quest (VIQ)
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,
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.
Eg: 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:
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 |
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.
Codomain is a set of all possible values of the given function that come out as a result.
Real numbers are all those which are positive, negative, and including zero. So zero is also a real number.
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.
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.
Application Date:09 September,2024 - 14 November,2024
Application Date:09 September,2024 - 14 November,2024
Application Date:01 October,2024 - 30 October,2024
Application Date:01 October,2024 - 30 October,2024
Register for Vidyamandir Intellect Quest. Get Scholarship and Cash Rewards.
As per latest 2024 syllabus. Physics formulas, equations, & laws of class 11 & 12th chapters
As per latest 2024 syllabus. Chemistry formulas, equations, & laws of class 11 & 12th chapters
Accepted by more than 11,000 universities in over 150 countries worldwide
Register now for PTE & Unlock 20% OFF : Use promo code: 'C360SPL20'. Valid till 15th NOV'24! Trusted by 3,500+ universities globally
As per latest 2024 syllabus. Study 40% syllabus and score upto 100% marks in JEE