Class 11 Maths Chapter 2 Relations and Functions – Revision Notes

Chapter 2, Relations and Functions, builds on the Cartesian product of two sets to define relations, and then narrows relations down to the special case of functions, where algebraic operations like addition and multiplication can also be applied.

Last Updated: September 23, 2026

Common Mistakes Students Make in Relations and Functions

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Key Concepts

The Cartesian product A×B is the set of all ordered pairs (a, b) where a belongs to A and b belongs to B, with |A×B| = |A|×|B|. A relation is simply any subset of A×B; its domain is the set of first elements used, and its range is the set of second elements. A function is a special kind of relation where every element in the domain maps to exactly one output — no domain element is allowed to have two different outputs. Common function types include the identity function f(x)=x, constant functions f(x)=c, the modulus function f(x)=|x|, the signum function (giving −1, 0 or 1), and the greatest integer function [x].

Quick Recap

• Every function is a relation, but not every relation is a function.
• A relation fails to be a function if any single domain element maps to more than one output.
• Functions can be combined algebraically: (f+g)(x), (f−g)(x), (fg)(x), and (f/g)(x) where g(x) ≠ 0.
• The domain of a combined function like f/g excludes any input where the denominator g(x) equals 0.

Quick visual: a worked diagram from the full Solutions page, for reference.

Common Mistake to Avoid

Students often assume every relation qualifies as a function. A relation only becomes a function if each input value is paired with exactly one output; if even one input maps to two different outputs, it is a relation but not a function.

Frequently Asked Questions

Q. What is the quickest way to check if a relation is a function?
For every input (x-value) in the relation, check that it appears with only one output (y-value); if any input repeats with a different output, the relation is not a function.

Full walkthrough: Chapter 2 Solutions · Extra Questions.

What to Revise First (and Last) in Relations and Functions

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Written by Satish

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