RD Sharma Class 12 Solutions Chapter 2 - Functions (Ex 2.1) Exercise 2.1

Students who want to perform well in the exam can benefit from RD Sharma Solutions Class 12 Maths Chapter 2 Functions. Experts created the solutions to boost students' confidence in understanding the concepts covered in this chapter and methods for solving problems in a shorter period. While practicing problems, students can access RD Sharma Solutions for step-by-step guidance and instant doubt clearance.

Class 12 Functions, Chapter 2 The function, domain, and codomain of functions are all explained by RD Sharma Solutions. It includes four exercises. Our subject experts prepare RD Sharma Solutions for Class 12 resources based on the Class 12 CBSE syllabus, taking into account the types of questions asked in the CBSE Class 12 board exam. Students can easily find solutions to problems in RD Sharma Solutions for Class 12. Let us take a look at some of the key concepts covered in this chapter.

Functions and Relationships Class 12 Chapter 1 statistics begin with a review of general notation for relations and functions. In class 11, students learned about domain, codomain, and range, as well as the various types of specific real-valued functions and their corresponding graphs. In class 12 Maths Chapter 1, students will learn in-depth about various types of relations and functions, function composition, and so on.

Class 12 Concepts of Relations and Functions

Relations and Functions for Class 12 cover the following topics and subtopics:

• Introduction

• Relationship Types

• Function Varieties

• Function composition and invertible functions

• Operations on binary numbers

Let us now go over the concepts of relation and function in greater depth.

Relation

The concept of relation is used to describe the relationship between two objects or quantities. If we consider two sets, the relationship between them will be established if there is a connection between the elements of two or more non-empty sets.

"A relation R from a set A to a set B is a subset of the cartesian product A B obtained by describing a relationship between the first element and the second element y of the ordered pairs in AxB," according to mathematics.

Relation’s Types

A relation R from A to A is also known as a relation on A, and the relation in a set A is known as a subset of AxA. As a result, the empty set and AxA are two extreme relations. The following are definitions of various types of relationships:

Empty Relation 

If no element of A is related to any other element of A, i.e. R =φ ⊂ AxA, the relation R in a set A is known as an empty relation.

Universal Relation

If every element of A is related to every other element of A, i.e. R = AxA, then the relation R in set A is said to be universal.

The empty relation and the universal relation are both referred to as trivial relations at times.

A relation R in a set A is called-

• Reflexive - if (a, a) ∈ R, for every a ∈ A,

• Symmetric - if (a1, a2) ∈ R implies that (a2, a1) ∈ R , for all a1, a2∈ A,

• Transitive - if (a1, a2) ∈ R and (a2, a3) ∈ R  implies that (a1, a3) ∈ R  for all a1, a2, a3 ∈ A.

Functions

A function is a relationship that explains why each input should have only one output. It is a type of relation (a set of ordered pairs) that follows a rule, namely that each y-value should be connected to only one other y-value.

"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," according to mathematics.

In other words, a function f is a relation from a set A to a set B where the domain of f is A and no two distinct ordered pairs in f share the same first element. A and B are also two non-empty sets.

We provide RD Sharma solutions for class 12 maths chapter 2 – functions to help students understand the various types of functions such as arithmetic function, constant function, signum function, onto function, and many functions in a very simplified manner. Prepare in detail all of the important concepts of functions using the complete exercise-by-exercise solved RD Sharma solutions provided here. The solutions and exercises will also assist students in effectively preparing for the exams. Experts have created RD Sharma solutions for class 12. The solutions are free, and students can view them online by clicking the links provided below, or they can save them for future use.