# Functions Class 11 Mathematics Solutions | Exercise - 2.3

## Chapter - 2  Functions

If you're learning math in grade 11, you might come across a chapter called "Functions." It's usually found in the second chapter in many textbooks. Sometimes, the problems in this chapter can be tricky, and you might get stuck. But don't worry! I have the answers to help you out with the problems in the function chapter.

In the function chapter, we will learn about finding the domain, range, and inverse of functions. This chapter has three exercises, and each exercise covers different subtopics related to the main topic, which is "function." Before we explore the solutions section, let's get a basic understanding of what functions are.

### Introduction of types of Algebraic Functions

Functions, that can be formed from a real variable x with the help of some algebraic operations such as addition, subtraction, multiplication, division and extraction of roots, are called the algebraic functions. Some special types of algebraic functions are defined below:

#### a. The Identity Function

Let A be any set. The function f:A→A defined by, y = f(x) = x for x ∊ A is called the identity function. It is usually denoted by Iₐ.

#### b. The Constant Function

Let A be any set and B = {c}. Then, the function f : A→B defined by y = f(x) = c for x ∊ A is called the constant function. In other words, a function is said to be a constant function if all its functional values are the same. (i.e if the range of the function is a singleton set).

If A = R the set of real numbers and c is a real number, the graph of y = f(x) = c is a straight line parallel to the x-axis at a distance of c units from the x-axis:

#### c. The Linear Function

Let A and B be any two sets. Then, a function f: A→B defined by y = f(x) = mx + c for x ∊ A, where m and c are constants, is called a linear function.

If A=B=R, the set of real numbers, the function defined by y= f(x)=x+1 is a linear function. Its graph is a straight as shown in figure given aside.

### Exercise - 2.3

Please note that this PDF focuses exclusively on Exercise 2.3. However, if you need solutions for other exercises, we've got you covered! Simply click the button above, and you'll find the solutions for those exercises as well. It's just a click away!

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## Is Class 11 Functions Note Helpful For Student ?

Absolutely! Our solutions for the Class 11 Mathematics Function Chapter are designed to greatly benefit students in their studies. Here are three key ways our solutions can help students excel in this subject:

### 1. Comprehensive Understanding

Our solutions provide students with a comprehensive understanding of the Function Chapter. Each step is explained in detail, guiding students through the problem-solving process. By following our solutions, students can grasp the underlying concepts and techniques required to tackle similar problems on their own.

### 2. Practice and Reinforcement

Practice is essential for mastering any subject, and mathematics is no exception. Our solutions offer a wealth of practice opportunities for students. By studying the solutions and attempting the problems independently, students can reinforce their learning, build confidence, and improve their problem-solving skills.

### 3. Exam Preparation

The solutions for the Function Chapter serve as an invaluable resource for exam preparation. Students can use these solutions as a reference to review concepts, learn alternative problem-solving approaches, and understand the expected format and presentation of solutions. By studying our solutions, students can gain insights into the types of questions that may appear in exams and develop strategies to approach them with confidence.

## How to secure good marks in Mathematics ?

As, you may know I'm also a student. Being a student is not so easy. You have to study different subjects simultaneously. From my point of view most of the student are weak in mathematics. You can take me as an example, I am also weak in mathematics. I also face problems while solving mathematics questions.

If you want to secure good marks in mathematics then you should practise them everyday. You should once revise all the exercise which are already taught in class. When you are solving maths problems, start from easy questions that you know already. If you do so then you won't get bored.

Maths is not only about practising, especially in grade 11 you to have the basic concept of the problem. When you get the main concept of the problem then you can easily any problems in which similar concept are applied.

When your teacher tries to make the concept clear by giving examples then all students tries to remember the same example but you should never do that. You can create your own formula which you won't forget later.

If you give proper time for your practise with proper technique then you can definitely score a good marks in your examination.

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