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RD Sharma Solutions

RD Sharma Class 12 Maths Solutions Chapter 2 - Functions

RD Sharma Class 12 Maths Solutions Chapter 2 - Functions

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An Overview Of Vedantu’s Class 12 Math Chapter - 2 Functions Solutions Of Rd Sharma

Functions are one of the most important Chapters for Class 12 students. It is the basics of calculus that we study in higher Classes. The free PDF of RD Sharma Class 12 Chapter 2 solutions are prepared by Vedantu experts to make the students understand easily. All solutions are particularly designed to provide students with a step-by-step approach so that they can prepare for their exams by referring to the solutions given.

Class 12 Mathematics Chapter 2

Students who want to get a decent academic score in the exams can take help from RD Sharma Solutions Class 12 Mathematics Chapter 2 at no cost. Experts created the solutions to help students gain confidence in their comprehension of the topics discussed in this Chapter and approaches for solving problems in a quicker time.

Our subject experts have prepared the RD Sharma Solutions for Class 12 solution based on the CBSE Class 12 syllabus and the types of questions asked in the CBSE Class 12 board exam. While working on problems, students can consult RD Sharma Solutions for step-by-step instructions and immediate clarification of doubts.

Class 12 Functions Chapter 2 Function, domain, and co-domain of functions are explained by RD Sharma Solutions. There are four exercises in all. Answers to the problems in RD Sharma Solutions for Class 12 are freely accessible to students.

Let's take a closer look at some of the key topics covered in this Chapter:

Classification of functions

Types of functions

Constant function
Identity function
Modulus function
Integer function
Exponential function
Logarithmic function
Reciprocal function
Square root function

Operations on real functions

Operations on real functions deals with the application of mathematical operations, that is to say,

Addition.
Subtraction.
Multiplication.
Division.

Kinds of functions

One-one function
On-to function
Many one functions
In to function
Bijection

Composition of functions

When Operation to function composes, a new function is referred to as a composition function. For example, if two operations A and B, compose a new function which is C, which is this manner c(x) = B(A(x)).

Properties of the composition of functions

Associative Properties.
Commutative Property.

The Inverse of a function

When B and A return the output, which is the value of input of B, then in such a case we can say that A is the inverse of B, and this is regarded as the inverse function.

The Inverse of an element

The inverse of an element refers to the concepts of the reversal of sign in relation with the addition, and also, in relation to the multiplication, it refers to the process of reciprocation. When the given element combines with another element it negates the effect of the combination.

Relation between graphs of a function and its inverse

When the function reverses the effect of another function, then it is referred to as the inverse of a function. The relation between the same, that is to say, function and its inverse, is obtained in the graph by the reflection of the original function graph, across the line, where, x = y.

A student can find anything and everything relevant to Chapter 2 of Class 12 Mathematics under this page. Vedantu has a staff of dedicated educators who are eager to pass on their knowledge and skills in the most efficient manner possible. Furthermore, if a student has any questions about Mathematics Class 12, they can click on to the website and submit their questions, as well as receive the RD Sharma Solution for Class 12 Mathematics Chapter 2 PDF edition. The experts are there for you if you need them, they will promptly respond and clear your doubts up.

What is a Function?

Let X and Y to be two non-empty sets. A function f from X to Y denoted as f: X → Y is a rule which says that each element x ∈ X is associated with a unique element y ∈ Y. f is thus defined as a function from X to Y.

The domain of f is composed of the elements of X, while the codomain of f is composed of the elements of Y. The range of X, which is a subset of Y, is the image of the element of X.

This free PDF of RD Sharma Solutions Class 12 Mathematics Functions is accessible on the Vedantu platform and has an exceptional solution to all of the textbook's problems.

While preparing RD Sharma Answers, Students should keep the Following Guidelines in Mind:

Before attempting the questions, we suggest students read them attentively. Since the questions from this Chapter-2 Functions contain a few tough questions, they may end up with the incorrect answer if the questions are not comprehended properly which can then cost them a lot of time

The Vedantu platform offers a free PDF that provides a step-by-step approach to a solution. As a result, students are advised to go over the content thoroughly without skipping any of the sections.

The RD Sharma Solutions for Class 12 Mathematics Chapter 2 contains a large number of exercise and practice problems that students can use to prepare for their exams. Read carefully all the questions and answers with a mind free of any stress or tension.

FAQs on RD Sharma Class 12 Maths Solutions Chapter 2 - Functions

1. How can using Vedantu's RD Sharma Class 12 Solutions for Chapter 2 help me master Functions?

Vedantu's RD Sharma Solutions for Class 12 Maths Chapter 2 provide a detailed, step-by-step approach to every problem. This helps you not only to verify your final answers but also to understand the precise methodology for proving properties like injectivity (one-one) and surjectivity (onto). By following these solutions, you can build problem-solving speed and confidence for your board exams.

2. Are the solutions for Chapter 2 Functions in RD Sharma Class 12 aligned with the latest CBSE 2025-26 syllabus?

Yes, Vedantu's RD Sharma solutions for Class 12 Maths Chapter 2 are fully updated to align with the CBSE syllabus for the 2025-26 academic year. They cover all prescribed topics, including types of functions, composition of functions, and invertible functions, ensuring your preparation is relevant and thorough.

3. How do the RD Sharma solutions explain the method to prove if a function is one-one (injective) or onto (surjective)?

The solutions provide a clear, structured method for proving the types of functions, which is crucial for scoring well. The typical approach demonstrated is:

For One-One (Injective): Assume f(x₁) = f(x₂) for any x₁, x₂ in the domain, and then algebraically prove that x₁ must equal x₂.
For Onto (Surjective): Assume an arbitrary element 'y' in the codomain and show that there exists an element 'x' in the domain such that f(x) = y.

The solutions apply this exact method to numerous examples, making the concept easy to master.

4. Why is it essential for a function to be both one-one and onto (bijective) to be invertible, as explained in the RD Sharma solutions?

The RD Sharma solutions implicitly show why a function must be bijective to have an inverse. The reasoning is:

If a function is not one-one, an output value would correspond to multiple input values. Its inverse would then have to map one input to multiple outputs, which violates the definition of a function.
If a function is not onto, there are elements in the codomain that are not mapped to by any element in the domain. The inverse function would be undefined for these elements.

Thus, only a bijective function guarantees a valid, well-defined inverse.

5. Beyond just solving for (gof)(x), how do the RD Sharma Chapter 2 solutions help in understanding the domain and range of composite functions?

While the solutions provide the final composed function, they fundamentally reinforce a critical concept for its existence. To define the composition g(f(x)), the range of the inner function f(x) must be a subset of the domain of the outer function g(x). By working through the diverse problems in the solutions, you gain practical experience in checking this condition, which is a key aspect of understanding composite functions deeply.

6. What is a common mistake students make when determining if a function is bijective, and how do the RD Sharma solutions help prevent it?

A very common mistake is to only check the algebraic properties of a function without considering its specified domain and codomain. For example, the function f(x) = x² is one-one if the domain is [0, ∞) but not if the domain is all real numbers (R). The RD Sharma solutions meticulously refer to the given domain and codomain in every problem, training you to always consider these constraints before concluding if a function is one-one or onto.

7. Do the RD Sharma Class 12 Maths Solutions for Chapter 2 cover the objective and MCQ-type questions?

Yes, the solutions cover all exercise problems from the RD Sharma textbook, including objective-type and Multiple Choice Questions (MCQs). For each MCQ, the solutions provide a detailed explanation of how to arrive at the correct option, which helps in developing the speed and conceptual clarity needed for the board exam's objective section.