# RS Aggarwal Class 12 Chapter 2 Solutions (Functions)

RS Aggarwal Solutions for Class 12 Chapter 2 Functions plays an important role while preparing for the CBSE & other competitive exams. It consists of diverse varieties of questions along with answers to help you boost your accuracy rate during the exam. The topics covered under these practice solutions are – types of functions, the composition of functions, and, invertible functions. Injective, Surjective and Bijective functions are also covered under the solutions of Chapter 2 Functions.

There are 4 exercises comprising a total of 31 questions of different kinds. The solutions are arranged exercise-wise to ease your search for an increasing level of difficulty. These solutions will help you to get an idea about the pattern of questions asked in various exams of your level. The answers of Class 12 Chapter 1 in RS Aggarwal are curated in the layman’s language to facilitate the process of building a strong base in Chapter ‘Functions’.

By making it a custom to practice the answers in RS Aggarwal Solutions for Class 12 Chapter 2 by Instasolv, you will get good marks in CBSE exams. The solutions are specifically prepared by the Maths expert after extensive research regarding the most frequently asked questions related to Functions. Therefore if you want in-depth coverage of the syllabus, these answers at Instasolv are the key enabler.

## Topics Covered in RS Aggarwal Solutions for Class 12 Chapter 2 **Introduction to Functions:**

The function is a concept which is of vital importance in not just maths but also in RS Aggarwal Class 12 Maths Solutions Functions. Some special functions that we learnt in previous classes are identity function, constant function, polynomial function, rational function etc. along with their graphs.

For Example, if A and B are two sets which are non-empty, then a function *f *is a subset of *A *x *B, *if the following conditions are satisfied:

- For all a ∈ A, there exists b ∈ B, such that (a, b) ∈ f; and
- No two ordered pairs in f have the same first element.

**Range and Domain:**

If we consider two non-empty sets A and B, and a function f which associates all elements of A to a unique element in B. Then, in function f, set A is the domain and set B is the co-domain. The set consisting of images of elements of the set A is called the range of function f.

**One-One Function:**

If a function f for two non-empty sets A and B is such that the elements of set A have unique images on set B, then f is known as One-One function or an injection.

It can be expressed as ƒ : A → B is injection implies that

a ⧧ b ⤇ ƒ(a) ⧧ ƒ(b) for all a, b ∈ A

Or, ƒ(a) = ƒ(b) ⤇ a = b for all a, b ∈ A

A function is generally one-one if it is either strictly increasing or strictly decreasing.

**Many-One Function:**

If more than one element of set A has the same image in the set B, then the function

ƒ is termed as a many-one function.

Therefore, ƒ : A → B will be a many-one function if,

x ⧧ y but ƒ(x) = ƒ(y).

Hence it can be concluded that if a function is not a one-one function then it will be a many-one function.

**Surjection (Onto Function):**

When the range of the function f is equal to its co-domain, or if ƒ(A) = B where A and B are two non-empty sets. In other words, function ƒ: A → B is a surjection if all the elements of B are an image of the elements of A.

If there is even one element in set B with no pre-image in the set A, then it is known as an Into Function.

**Bijection (One-One Onto Function)**

A given function f for two non-empty sets A and B, will be termed as a Bijection if it is onto and one-one simultaneously.

Therefore ƒ: A → B is a bijection if

- ƒ(x) = f(y) ⤇ x = y for each x, y ∈A
- ƒ(A)= B

**Highlights of this RS Aggarwal Maths Chapter – Functions**

- If, for a function ƒ : A → B, ƒ(A) ⧧ B, then ƒ : A → ƒ(A) is always an onto function.
- Two bijective functions always compose a bijective function.

### Exercise Wise Discussion of RS Aggarwal Solutions for Class 12 Chapter 2 Functions

- The exercise solutions of 2A will make you proficient in identifying the kind of function. You are required to show if a function is bijective, surjective or injective in most problems in this exercise.
- Exercise solutions for 2B will step up the difficulty level, where you will have to find the values of more complicated functions.
- The third exercise consists of the questions which are very short answer type and will help you revise the concepts of the types of functions in-depth.
- Last exercise 2D is about the invertibility of the functions.
- You should solve these exercises to stand out among your classmates.
- This topic is also of immense importance for competitive examinations, therefore practising these RS Aggarwal Solutions will prepare you for pan India competitions.

### Benefits of RS Aggarwal Solutions for Class 12 Maths Chapter 1 by Instasolv

- The subject matter expert team at Instasolv has made sure to simplify the most complicated questions in simple steps.
- The solutions at Instasolv are available free of cost.
- We make sure we have updated the solutions according to the latest CBSE guidelines and syllabus, and hence Instasolv should be the reliable and one-stop solution for all your doubts, that you are looking for.