Class 12 Maths - TAMILNADU
Relations and Functions
The Chapter 'Relations and Functions' in Class 12 Mathematics under Tamil Nadu Samacheer Kalvi builds upon Class 11 foundations by introducing advanced concepts like types of relations (reflexive, symmetric, transitive, and equivalence relations), types of functions, composition of functions, and invertibility. Students also explore binary operations and trigonometry-based inverse functions. This chapter is vital for board exams as it consistently features in both short-answer and 5-mark sections, laying the fundamental groundwork for calculus and higher mathematics.
Start Learning FreeKey Concepts
Equivalence Relation
A relation defined on a set that is simultaneously reflexive, symmetric, and transitive.
One-One Function (Injective)
A function where distinct elements in the domain have distinct images in the co-domain, meaning if f(x1) = f(x2), then x1 = x2.
Onto Function (Surjective)
A function where every element in the co-domain has at least one pre-image in the domain, meaning the range equals the co-domain.
Composition of Functions
The chaining of two functions where the output of one function becomes the input of another, denoted as (g o f)(x) = g(f(x)).
Inverse of a Function
A function that reverses another function, existing only if the original function is both one-one and onto (bijective).
Important Formulas
Board Exam Info
In the Tamil Nadu Samacheer Kalvi Class 12 Mathematics board exam, this chapter typically carries around 10 to 15 marks. Questions commonly include 1-mark objective queries, 2-mark or 3-mark problems checking equivalence relations or function composition, and major 5-mark questions proving invertibility or finding the inverse of a given function.
Frequently Asked Questions
How do I prove a relation is an equivalence relation?
You must mathematically prove three properties separately: Reflexivity (aRa for all a), Symmetry (if aRb then bRa), and Transitivity (if aRb and bRc then aRc).
What is the difference between One-One and Onto functions?
One-one means no two domain elements map to the same co-domain element. Onto means every co-domain element is used as an output.
When does a function have an inverse?
A function has an inverse if and only if it is a bijection, meaning it is both one-one (injective) and onto (surjective).
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