Relations and Functions — Class 12 Mathematics

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 is one-one if , and onto if every element of is the image of some element of . Composition of functions is introduced, and a bijection is shown to have an inverse satisfying . These ideas form the backbone for inverse trigonometric functions and for understanding invertibility throughout calculus and algebra.