Tamil Nadu Class 10 Maths Chapter 1 - Relations and Functions

Overview

This chapter builds the language of inputs and outputs used throughout higher maths. The key skill is recognising when a relation is a function and stating its domain and range correctly.

1. Ordered Pairs and Cartesian Product

• An ordered pair (a, b) keeps order — (a, b) ≠ (b, a) in general.
• Cartesian product: A × B = { (a, b) : a ∈ A, b ∈ B }.
• Size: n(A × B) = n(A) × n(B).

2. Relations

A relation from A to B is any subset of A × B. Its domain is the set of first elements; its range is the set of second elements.

3. Functions

A relation is a function if every element of the domain maps to exactly one element of the co-domain.

Types of functions:

• One-one (injective): different inputs give different outputs.
• Onto (surjective): every co-domain element is an output.
• Bijective: both one-one and onto.
• Also: constant, identity, and inverse functions.

4. Function Notation

If f(x) = 2x + 1, then f(3) = 2(3) + 1 = 7. The composition (f∘g)(x) = f(g(x)).

Worked Examples

Example 1 — Cartesian product

A = {1, 2}, B = {a, b, c}. Find A × B and n(A × B).

Example 2 — Domain and range

Find the domain and range of R = {(1,4),(2,5),(3,6),(2,7)}.

Example 3 — Is it a function?

Is R = {(1,2),(2,3),(1,4)} a function?

Example 4 — Evaluating a function

If f(x) = 3x − 5, find f(2) and f(−1).

Example 5 — Composition

If f(x) = x + 2 and g(x) = 2x, find (f∘g)(3).

Common Mistakes

• Writing (b, a) instead of (a, b) in the Cartesian product.
• Counting a repeated domain value twice in the domain set.
• Calling a relation a function when an input has two outputs.
• Confusing co-domain (target set) with range (actual outputs).

Exam Tips & Revision Checklist

• The function test: one input → one output.
• n(A × B) = n(A) × n(B) is a frequent one-mark question.
• Practised: Cartesian product, domain/range, function test, f(x) evaluation, composition.