NCERT Solutions for Class 12 Maths Chapter 1 Exercise 1.2 Relations and Functions - PDF Download

NCERT solutions class 12 maths chapter 1 exercise Relations and Functions consist of questions related to types of functions. Function is a very important topic in mathematics; therefore, it is necessary to study function and its types in detail. In Class 11, students are already familiar with the concept of special functions such as identity, constant, polynomial, rational, modulus, signum, etc. This chapter will further elucidate the relation between injective and surjective functions to make sure you understand the concepts and you will also learn the concepts of composition of functions and invertible functions. 

Class 12 maths chapter 1 exercise 1.2 NCERT solutions consists of a total of 12 questions based on types of functions. These questions are simple to attempt if you understand the concepts properly. Ex 1.2 class 12 maths solutions are designed by subject experts of eSaral to help you revise the concepts in simple language. Ex 1.2 class 12 maths Ch 1 is also accompanied by examples and illustrations that effectively explain the topic.

NCERT solutions class 12 maths chapter 1 ex 1.2 is available here in downloadable PDF format. These solutions PDFs have all the questions of ex 1.2 with their answers to help you score high marks in the board exam. You can download the free PDF from the given link below and make your preparation strong for final examination. 

Topics Covered in Exercise 1.2 Class 12 Mathematics Questions 

Ex 1.2 class 12 maths chapter 1 NCERT solutions describe the topic types of functions in detailed manner. 

1. Functions - A function is a relation that tells you that for each input, there is only one output. A function is a special type of relation (a collection of ordered pairs) that obeys a rule. For example, every y-value is connected to one y-value.

2. Types of Functions 

• One-One (or injective) Functions - A function f : X → Y is defined to be one-one (or injective), if the images of distinct elements of X under f are distinct,  i.e., for every x₁ , x₂ ∈ X, f(x₁ ) = f(x₂ ) implies x₁ = x₂ . Otherwise, f is called many-one.

• Onto (or surjective) Functions - A function f : X → Y is said to be onto (or surjective), if every element of Y is the image of some element of X under f, i.e., for every y ∈ Y, there exists an element x in X such that f(x) = y. 

• One-One and Onto (or bijective) Functions - A function f : X → Y is said to be one-one and onto (or bijective), if f is both one-one and onto.

3. Composition of Functions - Let f : A → B and g : B → C be two functions. Then the composition of f and g, denoted by gof, is defined as the function gof : A → C given by

                            gof (x) = g(f (x)), ∀ x ∈ A.

4. Invertible Function - A function f : X → Y is defined to be invertible, if there exists a function g : Y → X such that gof = I_X and fog = I_Y. The function g is called the inverse of f and is denoted by f ^–1. 

Thus, if f is invertible, then f must be one-one and onto and conversely, if f is one-one and onto, then f must be invertible. This fact significantly helps for proving a function f to be invertible by showing that f is one-one and onto, specially when the actual inverse of f is not to be determined.

Tips for Solving Exercise 1.2 Class 12 Chapter 1 Relations and Functions

Class 12 maths chapter 1 exercise 1.2 NCERT solutions are formulated by the academic team of maths with the highest level of accuracy to provide simple and precise understanding of the concepts and questions. Here are some most useful tips to solve ex 1.2 class 12 maths chapter 1 Relations and Functions.

1. Practicing the NCERT solutions of chapter 1 ex 1.2 will help students gain a deep understanding of all complex concepts with ease.

2. Students are advised to go through the topics and definitions provided in NCERT solutions properly. They help in promoting the fundamental knowledge of concepts that is  required to build a solid mathematical foundation.

3. The well-explained format of these solutions is beneficial in learning terms and definitions with questions. Solving the exercise questions and examples provided in the class 12 maths NCERT solutions chapter 1 will help you to establish a step wise understanding of each concept. 

Importance of Solving Ex 1.2 Class 12 Maths Chapter 1 Relations and Functions

Ex 1.2 class 12 maths chapter 1 provides understanding of types of functions. You will get numerous benefits by solving questions of exercise 1.2 class 12 maths. Some of the benefits are provided below.

1. NCERT solutions class 12 maths chapter 1 ex 1.2 has elaborated the concepts of functions, types of functions in precise and simple language so that students can get the conceptual knowledge of the topic.

2. Practicing questions in NCERT solutions will help you to solve each question with proper understanding of concepts that would be helpful for your board exams.

3. Students can use these solutions to revise the exercise 1.2 and get accurate answers on any question of ex 1.2 class 12 maths before the final exam.

4. NCERT class 12 maths ch 1 ex 1.2 solutions PDF provides questions with their answers which you can download for free from eSaral website and practice questions at your convenience.
   

Frequently Asked Questions 

Question 1. What concepts are discussed in NCERT solutions class 12 maths chapter 1 ex 1.2?

Answer 1. NCERT solutions class 12 maths chapter 1 ex 1.2 discusses types of functions such as one-one (or injective) functions,  onto (or surjective) functions, one-one and onto (or bijective) functions and composition of functions and invertible functions.

Question 2. Define Injective functions?

Answer 2. A function f : X → Y is defined to be one-one (or injective), if the images of distinct elements of X under f are distinct,  i.e., for every x₁ , x₂ ∈ X, f(x₁ ) = f(x₂ ) implies x₁ = x₂ . Otherwise, f is called many-one.

Question 3. Define Surjective functions?

Answer 3. A function f : X → Y is said to be onto (or surjective), if every element of Y is the image of some element of X under f, i.e., for every y ∈ Y, there exists an element x in X such that f(x) = y.