RS Aggarwal Class 12 Solutions Chapter-2 Functions

Class 12 RS Aggarwal Chapter-2 Functions Solutions - Free PDF Download

RS Aggarwal solutions class 12 functions is an important chapter in the maths curriculum for class 12. It plays a key role not only in the class 12 board exams but also in the competitive exams. RS Aggrawal solutions can help the students ace this topic and the experts at Vedantu have compiled these solutions in a methodical manner for the benefit of the students. If the students refer to these solutions and practice the questions, they can get good marks in their CBSE exams. The experts have prepared these solutions after extensive research and detailed study of the chapter. The solutions have been given according to the CBSE guidelines and include frequently asked questions on the topic of Functions in the exams.

RS Aggarwal Class 12 Maths Chapter 2

These solutions provide in-depth coverage of the syllabus and consist of a wide variety of questions along with step-by-step answers. Practising these questions will boost the accuracy rate of the students during the exam and give them the confidence to attempt all questions based on this topic. The solutions are available in an easy-to-download pdf format that the students can use for their revision. Students can access these solutions anytime and can use them for their class tests as well as their exam preparation.

Topics covered under these practice solutions:

Types of functions.
The composition of functions.
Invertible functions.
Injective, Surjective, and Bijective functions.

There are 4 exercises consisting of questions of different kinds and the solution to each question has been provided in a detailed step-by-step method. The solutions are arranged exercise-wise to facilitate easy reading. Since the questions in these solutions have been designed to cover all concepts related to functions, they will give an idea about the pattern of questions asked in various exams. The exercises include questions in increasing order of difficulty so that students have no difficulty solving each exercise.

Benefits of RS Aggarwal Class 12 Maths Chapter 2

The topic function is an important one not only from the point of view of the Class 12 board exams but also for the medical and engineering competitive examinations.
Practising these RS Aggarwal Solutions will prepare the students for all India competitions.
The varied type of questions helps the students get familiar with any type of question they may get in the exams.
The solutions have been provided in an easy to understand step by step format.

FAQs on RS Aggarwal Class 12 Solutions Chapter-2 Functions

1. How do Vedantu's RS Aggarwal Class 12 Maths Chapter 2 Solutions help in exam preparation for the 2025-26 session?

These solutions provide expertly crafted, step-by-step answers for every question in the textbook. This helps you understand the correct methodology for solving problems on Functions, identify common errors, and build confidence. Practising with these solutions ensures you cover the entire syllabus and are prepared for the types of questions asked in CBSE board exams.

2. What is the exercise-wise structure of RS Aggarwal Class 12 Maths Solutions for Chapter 2?

The solutions are organized by exercise to match the textbook, covering all key concepts of Functions.

Exercise 2A: Focuses on identifying different kinds of functions, such as injective, surjective, and bijective.
Exercise 2B: Involves solving problems to find the values of more complex functions.
Exercise 2C: Contains short answer questions for a thorough revision of function types.
Exercise 2D: Deals with the concept and problems related to the invertibility of functions.

3. What is a common mistake when determining if a function is invertible, and how do the solutions help prevent it?

A common mistake is trying to find an inverse without first proving the function is bijective (both one-one and onto). A function is only invertible if it is bijective. The RS Aggarwal solutions on Vedantu guide you through the correct two-step process: first, prove the function is one-one and onto, and only then proceed to find the inverse function, f⁻¹, which prevents this critical error.

4. What is the correct method to prove a function is one-one (injective) as shown in the Chapter 2 solutions?

The standard method demonstrated in the solutions is to assume that f(x₁) = f(x₂) for two arbitrary elements x₁ and x₂ in the domain. Then, through algebraic manipulation, you must prove that this implies x₁ = x₂. If this condition holds true for all elements, the function is proven to be one-one or injective.

5. Why is checking the co-domain essential when proving a function is 'onto' (surjective)?

The co-domain defines the entire set of possible output values. To prove a function is 'onto', you must show that for every element 'y' in the co-domain, there exists at least one element 'x' in the domain such that f(x) = y. If the range (the set of actual outputs) does not equal the co-domain, the function is not surjective. The solutions clarify this by showing how to express 'x' in terms of 'y' and confirming it belongs to the domain.

6. Do these solutions cover problems on the composition of functions like gof and fog?

Yes, the RS Aggarwal Class 12 Solutions for Chapter 2 provide detailed, step-by-step methods for solving problems involving the composition of functions. You will find clear explanations for calculating both gof(x) and fog(x), verifying their properties, and understanding their domains and ranges as per the CBSE syllabus.

7. How is the concept of a bijective function, explained in Chapter 2, applied in other areas of mathematics?

Understanding that a function must be bijective is crucial for the concept of invertible functions, which is fundamental in trigonometry (for inverse trigonometric functions) and calculus. A function must be both one-one and onto for its inverse to exist. This principle is a cornerstone for many advanced mathematical topics, ensuring that mappings between sets are consistent and reversible.