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# NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Exercise 2.3 - PDF Download

JEE Mains & Advanced

NCERT solutions class 11 maths chapter 2 Relations and Functions exercise 2.3 consists of questions related to the types of functions and the graphs associated with them. In this exercise, you will solve questions based on algebra of real function, and various formulas that are used to obtain the results. The identity function, polynomial, rational, modulus, greatest integer, and constant are analyzed in detail, along with their associated graphs. Class 11 maths chapter 2 exercise 2.3 NCERT solutions have provided numerous examples and questions to help you with the understanding of the fundamentals of functions.

Ex 2.3 class 11 maths chapter 2 solutions has 5 questions that are easy to solve. Class 11 maths chapter 2 ex 2.3 NCERT solutions have been structured in such a way that each concept is elucidated precisely to provide explicit knowledge. Ex 2.3 class 11 maths ch 2 solutions provided by eSaral explains each concept in detail so that you can prepare for examination and score good marks. NCERT solutions class 11 maths chapter 2 ex 2.3 are also available in PDF format. You must download the free PDF of these solutions from eSaral and practice chapter 2 ex 2.3 questions without any doubt. Download the PDF from the link provided below link.

## Topics Covered in Exercise 2.2 Class 11 Mathematics Questions

NCERT solutions chapter 2 Relations and Functions ex 2.3 is based on topics such as functions and their graphs, algebra of real functions.

 1 Functions Some functions and their graphs Algebra of real functions
1. Functions - 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.

In other words, a function f is a relation from a non-empty set A to a non-empty set B such that the domain of f is A and no two distinct ordered pairs in f have the same first element.

If f is a function from A to B and (a, b) ∈ f, then f (a) = b, where b is called the image of a under f and a is called the preimage of b under f.

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.

• Some functions and their graphs

(i) Identity function - Let R be the set of real numbers. Define the real valued function f : R → R by y = f(x) = x for each x ∈ R. Such a function is called the identity function.

(ii) Constant function - A function f: R → R by y = f (x) = c, x ∈ R where c is a constant and each x ∈ R. Here the domain of f is R and its range is {c}.

(iii) Polynomial function - A function f : R → R is said to be polynomial function if for each x in R, y = f (x) = a0 + a1 x + a2x2 + ...+ anxn , where n is a non-negative integer and a0 , a1 , a2 ,...,an∈R.

(iv) Rational functions - Rational functions are functions of the type $\frac{f(x)}{g(x)}$ , where f(x) and g(x) are polynomial functions of x defined in a domain, where g(x) ≠ 0.

(v) The Modulus function - The function f: R→R defined by f(x) = |x| for each x ∈R is called a modulus function. For each non-negative value of x, f(x) is equal to x. But for negative values of x, the value of f(x) is the negative of the value of x. I.e.,

f(x)= x,x0

-x,x<0

(vi) Signum function - The function f:R→R defined by

f(x) = 1, if x>0

0, if x=0

-1, if x<0

is called the signum function. The domain of the signum function is R and the range is the set {–1, 0, 1}.

(vii) Greatest integer function - The function f: R → R defined by f(x) = [x], x ∈R assumes the value of the greatest integer, less than or equal to x. Such a function is called the greatest integer function.

• Algebra of real functions

Here, you will learn how to add two real functions, subtract a real function from another, multiply a real function by a scalar (here by a scalar we mean a real number), multiply two real functions and divide one real function by another.

(i) Addition of two real functions -  Let f : X → R and g : X → R be any two real functions, where X ⊂ R. Then, we define (f + g): X → R by

(f + g) (x) = f (x) + g (x), for all x ∈ X

(ii) Subtraction of a real function from another -  Let f : X → R and g: X → R be any two real functions, where X ⊂ R. Then, we define (f – g) : X→R by (f–g) (x) = f(x) –g(x), for all x ∈ X.

(iii) Multiplication by a scalar - Let f : X→R be a real valued function and α be a scalar. Here by scalar, we mean a real number. Then the product α f is a function from X to R defined by (α f ) (x) = α f (x), x ∈X.

(iv) Multiplication of two real functions - The product (or multiplication) of two real functions f:X→R and g:X→R is a function fg:X→R defined by (fg) (x) = f(x) g(x), for all x ∈ X.

This is also called pointwise multiplication.

(v) Quotient of two real functions - Let f and g be two real functions defined from X→R, where X ⊂ R. The quotient of f by g denoted by $\frac{f}{g}$  is a function defined by,$\left(\frac{f}{g}\right)(x)=\frac{f(x)}{g(x)}$  provided g(x) ≠ 0, x ∈ X

## Tips for Solving Exercise 2.3 Class 11 Chapter 2 Relations and Functions

Ex 2.3 class 11 maths chapter 2 involves some useful tips and tricks to solve ex 2.3 questions. You can find them below.

1. You'll get a better understanding of how functions work, type of functions, and type of formulas. These formulas are good for helping you figure out which formula is best for a certain kind of question.

2. Practicing with NCERT solutions on a regular basis will also help you get better at recognizing the different functions and their graphs.

3. This exercise will provide students with the opportunity to clarify any questions they may have regarding fundamental concepts and functions, allowing them to progress their knowledge in a timely and precise manner.

## Importance of Solving Ex 2.3 Class 11 Maths Chapter 2 Relations and Functions

There are a lot of benefits of solving questions of ex 2.3 class 11 maths chapter 2 relations and functions. You will find some advantages provided by subject experts of eSaral.

1. NCERT solutions class 11 maths chapter 2 provides precise knowledge of functions and their graphs, algebra of real functions which will help you to understand each question of ex 2.3.

2. The NCERT solutions for class 11 maths ex 2.3 questions provide a comprehensive, sequential explanation to assist students in understanding the solutions to the exercise questions.

3. By practicing questions in NCERT solutions class 11 maths ch 2 ex 2.3, you will be well-versed with the concepts of functions.

4. Solving questions in NCERT solutions exercise 2.3 will develop problem solving skills.

#### Frequently Asked Questions

Question 1. What is Function?

Answer 1. 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.

Question 2. What is a polynomial function?

Answer 2. A polynomial is a function in which only the positive integer exponents of a variable are included in an equation.

Question 3. What do you mean by modulus function?

Answer 3. A modulus function is the absolute value of a variable or number that has been given as the input to the function.