RD Sharma Class 11 Solutions Chapter 3 - Functions (Ex 3.1) Exercise 3.1 - Free PDF

Q: 2. Explain with example domain, codomain and range in a function?

Let us consider a function, f(x) = 5xNow we will consider different values for a, for which we will get different output for function f(a), If x = 1, then f(1) = 5(1) = 5If x = 2, then f(2) = 5(2) = 10If x = 3, then f(3) = 5(3) = 15Here we can see that if the input is given as 1 then the output will be 5, so 1 is the domain and 5 is the range for that domain.Codomain is referred to as the range of function along with a few additional values whereas range is the subset of the codomain. It is quite hard to differentiate but range is the actual output whereas range has possible sets of output. Domain and range are nothing but input and output respectively. But the collection of possible outputs i.e. (5,10,15) are the codomains of the function.

RD Sharma Solutions

RD Sharma Class 11 Solutions Chapter 3 - Functions (Ex 3.1) Exercise 3.1 - Free PDF

Last updated date: 17th Apr 2024

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Preparation with RD Sharma Class 11 Solutions

Free PDF download of RD Sharma Class 11 Solutions Chapter 3 - Functions Exercise 3.1 solved by Expert Mathematics Teachers on Vedantu.com. All Chapter 3 - Functions Ex 3.1 Questions with Solutions for RD Sharma Class 11 Maths to help you to revise complete Syllabus and Score More marks. Register for online coaching for IIT JEE (Mains & Advanced) and other Engineering entrance exams.

RD Sharma Class 11 Solutions Chapter 3

RD Sharma Class 11 Solutions Chapter 3 Functions are for students studying in class 11th and will appear in the CBSE and many other All India competitive exams such as IIT- JEE. Solutions provided in RD Sharma Class 11 for chapter 3 will help you to obtain your goal and it will help you to solve problems of different difficulty levels as well as in practical life problems.

There are 6 exercises in the chapter and a total of 118 questions. Understanding the concepts of functions is very important as there are at least one or two questions from RD Sharma Class 11 Solutions Chapter 3 - Functions in your exams for sure. A function is a relation where the first element of any two ordered pairs cannot be repeated. It is a known fact that all functions are relations but then not all relations can be functions. A function can associate every element in its domain with only one element in its range.Marks weightage from this chapter in CBSE board examination is between 8 to 12 marks. This chapter sets up the basic foundation which is needed for differential and integral calculus. In this chapter, the students will be able to understand the concept of the function, domain, co-domain, range, equal and real functions, etc.

Example to Determine if the Following is a Function or Not

Given below are three sets- Set A, Set B, Set C, find which is a function.

a) A = {(1, 3), (2, 6), (3, 8), (4, 9)}

b) B = {(1, 2), (0, 3), (2, 5), (4, 2)}

c) C = {(1, 5), (2, 6), (1, 8), (7, 3)}

Solution:

a) A = {(1, 3), (2, 6), (3, 8), (4, 9)} is a function since every first element is different.

b) B = {(1, 2), (0, 3), (2, 5), (4, 2)} is a function since every first element is different. (The second element and first element can be same)

c) C = {(1, 5), (2, 6), (1, 8), (7, 3)} is not a function because the first element, 1 is repeated twice.

Important Concepts Discussed in this Chapter

All Functions which are also relations.
Definition of a function with examples.
Co-domain, domain and range of a function.
Equal functions and real functions.
The domain and range of real functions.
Standard real functions and their graphical representation.
The operations performed on real functions.

Exercises Links and number of questions in RD Sharma Class 11 Chapter 3- Functions are given below,

Here at Vedantu you will find solutions to every RD Sharma Class 11 chapters

Exercise 3.1 - 9 questions
Exercise 3.2 - 6 questions
Exercise 3.3 - 3 questions
Exercise 3.4 - 5 questions

FAQs on RD Sharma Class 11 Solutions Chapter 3 - Functions (Ex 3.1) Exercise 3.1 - Free PDF

1. What are the types of functions in RD Sharma Class 11 Chapter 2?

There are 4 types of functions in RD Sharma Class 11 Chapter 2 namely,

One to one function or Injective function
Many to one function
Onto Function or Surjective function
One-one correspondence or Bijective function
RD Sharma Class 11 provides detailed information regarding this chapter along with the solved questions and several other examples. Identify the input and output values, If each input value leads to one and only one output value, then the relationship is classified as a function but if any input value leads to two or more outputs, then do not classify the relationship as a function.

2. Explain with example domain, codomain and range in a function?

Let us consider a function, f(x) = 5x

Now we will consider different values for a, for which we will get different output for function f(a),

If x = 1, then f(1) = 5(1) = 5

If x = 2, then f(2) = 5(2) = 10

If x = 3, then f(3) = 5(3) = 15

Here we can see that if the input is given as 1 then the output will be 5, so 1 is the domain and 5 is the range for that domain.

Codomain is referred to as the range of function along with a few additional values whereas range is the subset of the codomain. It is quite hard to differentiate but range is the actual output whereas range has possible sets of output. Domain and range are nothing but input and output respectively. But the collection of possible outputs i.e. (5,10,15) are the codomains of the function.