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The Quickest and Easiest Way to Learn Relations and Functions-Class 12

Updated: May 28

relations and functions cover pic

Tips and Tricks to study Relations and Functions for Class 12

Learn how to prepare Relations, Functions and Inverse Trigonometric Functions for Class 12 Mathematics NCERT, ISC and CUET . These are the first 2 chapters of Class 12 Mathematics and they form the foundation for Calculus.

This blog gives you all the concepts that you need to know to get that above 90 percent in your exams. To start with, you learn the basic concept of a Relation.

Types of Relations

There are 3 standard Relations which you will need to know, namely, the Identity Relation, Empty Relation and Universal Relation. Questions on these could be asked in Multiple choices.

The next thing which you will need to learn is about the 3 types of Relations, namely, Reflexive, Symmetric and Transitive Relations and Equivalence Relations. You will also need to learn about Equivalence classes.

What is a function and why is it a Relation?

You will then proceed to learn about Functions and how Functions are derived from Relations. It is important to master this concept since logical questions can be asked on this topic. The 4 different types of functions, one to one, onto, many to one and into need to be learnt.

injective function test

You need to emphasize and learn more about injective and surjective functions which in turn will lead to to bijective functions . Bijective functions will lead you to the study of finding the inverse of a function. In this context you will also learn about composite Functions.

A few important formulas which will help you in problem solving!

important formulas in Relations and functions

So that's all about Relations and functions. The next chapter that you will need to learn is Inverse Trigonometric Functions. Since you know that the inverse of a function exists only if it is bijective, you need to check if the inverse Trigonometric Functions are bijective.

Inverse Trigonometric Functions: What you need to know

A very important concept of Inverse Trigonometric Functions that you will need to learn is the domain and range of each of the 6 inverse Trigonometric Functions. Based on this, you will solve problems on how to calculate the principal values. The properties on calculating the negative of inverse Trigonometric angles is also something that you should know along with composite of Inverse Trigonometric Functions.

domain and range of inverse trigonometric functions

Addition and Subtraction formulas of sin inverse, cos inverse and tan inverse are important formulas for you to remember. It is also important to learn formulas involving 2 tan inverse in terms of sin inverse, cos inverse and tan inverse. There are also formulas involving 3 sin inverse, 3 cos inverse and 3 tan inverse which should be included as part of your study.

properties of inverse trig functions
properties of 2 tan inverse

Application of all these concepts and formulas in problem solving is what will help you in your exam preparation.

Online tutoring if you need more help!

You can contact me for online tutoring if you want any extra help. All my students have done well in Mathematics and enjoyed the learning in the process. You can choose between one to one tutoring or group tutoring

To make math education universally accessible and affordable, I am conducting an online coaching class. for this topic. The entire course topic of Relations and Functions and Inverse Trigonometric Functions and would take about 10 sessions to complete. To start the session, there has to be a minimum of ten participants.

If you are interested, you can message me on for payment details and other relevant information.

Free resources on Relations and Functions Class 12.

Motivating you to learn Mathematics and like it ! Share the word around to any class 12 Math student who needs that little bit of help.

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