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In every school, each student has a unique ID number, and in the school’s database, that ID number represents the relation to that specific student. Similarly, in Mathematics, the Relations and Functions chapter discusses the connection between elements of two sets and their mapping. Also, this chapter includes the domain, co-domain, range, and graphing of a function. Relations and Functions Class 11 Notes are useful for calculus chapters (Differentiation and Integration) as well as algebra and coordinate geometry. The main purpose of these NCERT Notes of the Relations and Functions class 11 PDF is to provide students with an efficient study material from which they can revise the entire chapter.
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After going through the textbook exercises and solutions, students need a type of study material from which they can recall concepts in a shorter time. Relations and Functions Class 11 Notes are very useful in this regard. In this article about NCERT Class 11 Maths Notes, everything from definitions and properties to detailed notes, formulas, diagrams, and solved examples is fully covered by our subject matter experts at Careers360 to help the students understand the important concepts and feel confident about their studies. These NCERT Class 11 Maths Chapter 2 Notes are made in accordance with the latest CBSE syllabus while keeping it simple, well-structured and understandable. For the syllabus, solutions, and chapter-wise PDFs, head over to this link: NCERT.
Use the link below to download the Relations and Functions Class 11 Notes PDF for free. After that, you can view the PDF anytime you desire without internet access. It is very useful for revision and last-minute studies.
Understanding how elements connect and interact with each other is at the heart of mathematics, and NCERT Class 11 Maths Chapter 2: Relations and Functions lays the foundation for just that.
Ordered Pair: Two elements form an ordered pair.
Representation: (a,b)
NOTE: 2 ordered pairs (a, b) and (c, d) are said to be equal if (a=c) and (b=d)
If sets A and B have an ordered pair of (a,b) where aA and bB are called the Cartesian product.
Denoted by: A x B
Set builder form: A x B ={(a,b) : a ∈A and b∈ B}
NOTE:
If A=∅ , B= ∅, then the cartesian product A x B=∅.
It doesn’t satisfy the commutative law: (A, B)≠(B, A)
If either of the two sets is an infinite set, then the whole product becomes infinite.
A = infinite, B = finite, then A x B and B x A 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(A x B) = 6.
A group of ordered pairs containing one element from each set is called a relation between two sets. Suppose A, and B are both non-empty sets, then the relation is a subset of the Cartesian product of (A x B).
A subset is a relation between the first and second elements of ordered pairs in A x B.
The set of first elements in relations is called the domain, and the next element is called the image or range of R.
Set builder form: R={(a,b): (a,b)∈R}
Note:
Sets A and B are both non-empty sets with
Set builder form :
The domain of the relation R will be the range of the inverse relation
A relation F from A to B is called a function if every element in set A of a function has only one image in set B of a function.
A relation
In other words, a function
The notation
The set of all values of
range of
Function denoted as f: A→B is said to be a real-valued function if B is a subset of R . If A, and B are subsets of R, in such conditions, we can call f 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 belonging 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.
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 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
Domain:
Range :
Signum Function:
Real function f: R → R is said to be a 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 a rational 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 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.
Subtraction Of Real Functions:
If f: X → R and g: X → R are real functions, then we represent : (f – g): → R as (f – g) (x) = f (x) – g(x) where x belongs to X.
Multiplication Of Scalar:
If f: X → R is a real function, K is any scalar
The product of Kf is defined by : (Kf)(x) = Kf(x)
Multiplication Of Two Real Functions:
If f: → R and g: X→ R are real functions,
The product of the two functions is defined by: (fg) x = f(x). gx)
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 the NCERT Class 11 Maths Chapter 2 Notes.
Given below are some previous year question answers of various examinations from the NCERT class 11 chapter 2, Relations and Functions:
All the links of chapter-wise notes for NCERT class 11 maths are given below:
After finishing the textbook exercises, students can use the following links to check the NCERT exemplar solutions for a better understanding of the concepts.
Students can also check these well-structured, subject-wise solutions.
Students should always analyse the latest CBSE syllabus before making a study routine. The following links will help them check the syllabus. Also, here is access to more reference books.
A relation is a connection between elements of two sets, defined as a subset of their Cartesian product. It consists of ordered pairs where each pair shows how an element from one set is related to an element of another.
For sets A and B, the Cartesian product A × B includes all ordered pairs (a, b) where a∈A and b∈B.
Use the vertical line test, if any vertical line touches the graph more than once, it's not a function.
Relations and Functions Class 11 Notes are very important study materials for revision. These NCERT Class 11 Maths Chapter 2 Notes are made in accordance with the latest CBSE syllabus while keeping it simple, well-structured and understandable. These notes provide everything from definitions and properties to detailed notes, formulas, diagrams, and solved examples of the chapter.
The domain of a function is the set of all possible input values (x-values) for which the function is defined.
The range is the set of all possible output values (f(x)) that the function can produce from its domain.
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Exam Date:22 July,2025 - 28 July,2025
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