Chapter 1: Relations and FunctionsClass 12 Mathematics — summary, notes, extra questions & MCQ quiz

Summary

This chapter deepens the study of relations and functions begun in Class 11. A relation on a set is examined for the properties of being reflexive, symmetric and transitive; a relation that is all three is called an equivalence relation, and it partitions the set into disjoint equivalence classes. The chapter then classifies functions as one-one (injective), onto (surjective) and bijective. A function \(f:A\to B\) is one-one if \(f(x_1)=f(x_2)\Rightarrow x_1=x_2\), and onto if every element of \(B\) is the image of some element of \(A\). Composition of functions \((g\circ f)(x)=g(f(x))\) is introduced, and a bijection is shown to have an inverse \(f^{-1}\) satisfying \(f^{-1}\circ f=I\). These ideas form the backbone for inverse trigonometric functions and for understanding invertibility throughout calculus and algebra.

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