# Relations and Functions Notes, Class 11 Mathematics | SwaVid Relations and Functions, NCERT Class 11 Mathematics: notes with key ideas, formulas, common mistakes and 3 quick checks with worked answers. Canonical: https://www.swavid.com/cbse/class-11/maths/chapter/relations-and-functions Source: https://www.swavid.com/cbse/class-11/maths/chapter/relations-and-functions # Relations and Functions ## Formulas and definitions ## Key ideas ## Common mistakes ## Quick checks ## Keep going ## Questions parents ask ## Class 11 Mathematics on SwaVid ### Cartesian product of sets ### Relations ### Functions ### Standard real-valued functions ### Algebra of real functions ### Next chapter ### Related chapter ### Related chapter ### All chapters SwaVid › CBSE › Class 11 › Mathematics › Relations and Functions Notes written by SwaVid from the NCERT textbook. Class 11 Mathematics, Chapter 2. Key ideas, formulas and common mistakes. CBSE does not print marks for a single chapter. Short answer. This chapter introduces Cartesian products of sets, relations, and the concept of functions as special relations. Students learn to determine domains, ranges, and codomains, and study standard real functions along with their graphs and algebraic operations. Source: NCERT Mathematics (Reprint 2026-27) , Chapter 2, Relations and Functions For non-empty sets A and B, the Cartesian product A × B is the set of all ordered pairs (a, b) such that a belongs to A and b belongs to B. If set A has p elements and set B has q elements, then A × B has p × q elements. A relation R from a non-empty set A to a non-empty set B is a subset of the Cartesian product A × B. The set of all first elements in the ordered pairs of R is the domain, while the set of all second elements is the range. The whole set B is called the codomain. A relation f from a set A to a set B is a function if every element of set A has one and only one image in set B. No two distinct ordered pairs in a function can have the same first element. The chapter studies specific functions on real numbers including the identity function, constant function, polynomial function, rational function, modulus function, signum function, and greatest integer function, along with their domains, ranges, and graphs. Two real functions f and g can be added, subtracted, multiplied by a scalar, multiplied together, or divided. The operations are defined point-wise, with quotient (f / g)(x) = f(x) / g(x) defined only where g(x) ≠ 0. Try each question first. Then tap it to see the answer. Equate the first coordinates: x / 3 + 1 = 5 / 3 x / 3 = 5 / 3 - 1 = 2 / 3, so x = 2 Equate the second coordinates: y - 2 / 3 = 1 / 3 y = 1 / 3 + 2 / 3 = 1 x = 2, y = 1 n(A × B) = n(A) × n(B) = 2 × 3 = 6 The total number of relations is the number of subsets of A × B, which is 2^(n(A × B)) 2^6 = 64 n(A × B) = 6, total relations = 64 For f(x) to be real, the expression under the square root must be non-negative: 9 - x² ≥ 0 Rewrite as x² - 9 ≤ 0, which factors to (x - 3)(x + 3) ≤ 0 The inequality holds for values of x from -3 to 3 inclusive [-3, 3] Trigonometric Functions . Sets . Limits and Derivatives . The 14 chapters of Class 11 Mathematics . The CBSE Class 11 Maths curriculum says it gives no chapter or unit-wise weightage. Theory is 80 marks, plus 20 for internal assessment. No. They are written by SwaVid from the NCERT textbook. The CBSE curriculum is the reference for what is assessed. Trigonometric Functions. SwaVid is an AI tutor for Indian students in Classes 6 to 12. It finds the earlier ideas a child missed, then teaches today’s chapter. Start free to see how it works. - Ch 2 NCERT book - 80 marks, theory paper - 3 quick checks - Confusing range with codomain . The codomain is the entire target set B, whereas the range contains only those elements of B that are images of elements in A. The range is always a subset of the codomain. - Treating an ordered pair like a two-element set . In a set, {a, b} = {b, a}. In an ordered pair, order matters, so (a, b) does not equal (b, a) unless a = b. - Classifying a relation with repeated first elements as a function . Check that each input has exactly one output. If an input x is paired with two distinct outputs y₁ and y₂, the relation is not a function. - Ignoring zero denominators when dividing functions . The domain of (f / g)(x) is the intersection of the domains of f and g excluding all points where g(x) = 0. ## Key Links - [CBSE](https://www.swavid.com/cbse) - [Class 11](https://www.swavid.com/cbse/class-11) - [Mathematics](https://www.swavid.com/cbse/class-11/maths/chapters) - [Start free →](https://www.swavid.com/signup) - [All 14 chapters](https://www.swavid.com/cbse/class-11/maths/chapters) - [NCERT Mathematics (Reprint 2026-27)](https://ncert.nic.in/textbook.php) - [Open notes](https://www.swavid.com/cbse/class-11/maths/chapter/trigonometric-functions) - [Open notes](https://www.swavid.com/cbse/class-11/maths/chapter/sets) - [Open notes](https://www.swavid.com/cbse/class-11/maths/chapter/limits-and-derivatives) - [Class 11 Mathematics](https://www.swavid.com/cbse/class-11/maths/chapters) - [Start free →](https://www.swavid.com/signup)