NCERT Solutions for Class 12 Maths Chapter 1 Exercise 1.2 Relations and Functions  PDF Download
JEE Mains & AdvancedNCERT 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 
2. 
Types of Functions 
3. 
Composition of Functions 
4. 
Invertible Function 

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 yvalue is connected to one yvalue.

Types of Functions

OneOne (or injective) Functions  A function f : X → Y is defined to be oneone (or injective), if the images of distinct elements of X under f are distinct, i.e., for every x_{1} , x_{2} ∈ X, f(x_{1} ) = f(x_{2} ) implies x_{1} = x_{2} . Otherwise, f is called manyone.

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.

OneOne and Onto (or bijective) Functions  A function f : X → Y is said to be oneone and onto (or bijective), if f is both oneone and onto.

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.

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 oneone and onto and conversely, if f is oneone and onto, then f must be invertible. This fact significantly helps for proving a function f to be invertible by showing that f is oneone 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.

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

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.

The wellexplained 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.

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.

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.

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.

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 oneone (or injective) functions, onto (or surjective) functions, oneone 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 oneone (or injective), if the images of distinct elements of X under f are distinct, i.e., for every x_{1} , x_{2} ∈ X, f(x_{1} ) = f(x_{2} ) implies x_{1} = x_{2} . Otherwise, f is called manyone.
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.
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