Once upon a time, in a beautiful village called Mathville, there lived two best friends Alan and Betty. Alan was a dedicated baker and Betty, an enthusiastic gardener. Each time Alan would bake a delicious pastry, Betty would plant a beautiful flower.
Each pastry that Alan baked corresponded to a particular flower that Betty planted thus establishing a relation. Thus different types of relations such as one to one, onto and many to one could be explained by the relation between the pastries and flowers. The concept of functions was also introduced by associating each pastry with exactly one flower.
The story progresses to explaining domain and range where the domain consisted of all the pastries which Alan could bake and the range comprising all the flowers which Betty could plant. The story continues to unfold by illustrating concepts such as composite functions, invertibility and the identity function.
In short, understanding Relations and functions is a mutual exchange of talents. This illustrates the beauty of Relations and Functions in our everyday lives..
Here are Tips in Mathematics which will give you an exact idea of the topics that you should prepare for in Relations and Functions-Class 12 Maths NCERT. This is keeping in mind the changes prescribed by the NCERT board for the academic year 2023-24. To start with, you need to know that 2 chapters, namely , Relations and Functions and Inverse Trigonometric Functions comprise this topic.
What is a Relation
The 3 basic examples of a Relation namely, the Universal Relation, Empty Relation and Identity Relation.
Types of Relations:Reflexive, Symmetric and Transitive
Equivalence Relations and Equivalence Classes
Functions
Types of functions- Injective and Surjective
Bijective functions
In this context, you need to know a few important points such as:
Number of bijective functions from a finite set A to a finite set B.
Number of injective and surjective functions from a finite set A to a finite set B.
How to find the number of relations and functions from a set A to a set B.
Calculate the equivalence relations on a set containing 2 or 3 elements.
Resources for Relations and Functions
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Moving on to Inverse Trigonometric Functions, first and foremost, you will need to identify the graphs of the 6 inverse trigonometric functions, inverse sin, inverse cos, inverse tan, inverse cot, inverse sec and inverse cosec and most important, identify their domain and range.
Calculating the principal values is the next important point that you will need to learn. Once you get an idea of this, you will be able to solve any number of questions based on these. Questions can be twisted and turned in any way here but basically they all follow the same principle.
The next very important point to learn is how to use the Substitution method to simplify an Inverse Trigonometric Function. Note that, this concept is used extensively in Calculus, so you need to understand and learn it well.
You will also need to know a few basic formulas such as composite of an inverse trigonometric function with its inverse.
Using these concepts, you have a variety of questions asked in the form of MCQ'S, Case study based questions, assertion and reasoning based questions and long answer questions, Basically once you get the basic points clear, you will be able to answer any question in whichever way it is framed.
So, these are the important topics in Relations and Functions-Class 12 Mathematics NCERT that you should learn.
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