Relations and Functions
The Chapter Relation and Functions discusses the introduction of relations and functions, types of relation, types of functions, the composition of functions and invertible function, binary operations, inverse function, and miscellaneous examples.
- Relations: A relation R is the subset of the cartesian product of A × B, where A and B are two non-empty elements. It is derived by stating the relationship between the first element and second element of the ordered pair of A × B.
- Inverse of Relation: A and B are any two non-empty sets. Let R be a relationship between two sets A and B. The inverse of relation R indicated as R-1, is a relationship that connects B and A and is defined by
R-1 ={(b, a) : (a, b) ∈ R}
where, Domain of R = Range of R-1 and Range of R = Domain of R-1.
- Functions: A relation f from a set A to set B is said to be a function if every element of set A has one and only image in set B.
- A cartesian product A × B of two sets A and B is given by: A × B = { (a,b): a ϵ A, b ϵ B}
- If (a, b) = (x, y); then a = x and b = y
- If n(A) = x and n(B) = y, then n(A × B) = xy and A × ϕ = ϕ
- The cartesian product: A × B ≠ B × A.
- A function f from set A to set B considers a specific relation type where every element x in set A has one and only one image in set B. A function can be denoted as f: A → B, where f(x) = y.
- Algebra of functions: If the function f: X → R and g: X → R; we have:
- (f + g)(x) = f(x) + g(x) ; x ϵ X
- (f – g)(x) = f(x) – g(x)
- (f . g)(x) = f(x).g(x)
- (kf)(x) = k(f(x)) where k is a real number
- {f/g}(x) = f(x)/g(x), g(x)≠0
Learn More, Domain and Range of a Function
Class 12 Maths Formulas
Class 12 maths formulas page is designed for the convenience of the learners so that one can understand all the important concepts of Class 12 Mathematics directly and easily. Math formulae for Class 12 are for the students who find mathematics to be a nightmare and difficult to grasp. They may become hesitant and lose interest in studies as a result of this. We have included all of the key formulae for the 12th standard Maths topic, which students may simply recall, to assist them in understanding Maths in a straightforward manner. For all courses such as Integration, Differentiation, Trignometry, Relation and Functions, and so on, the formulae are provided here according to the NCERT curriculum.
Table of Content
- Chapter 1: Relations and Functions
- Chapter 2: Inverse Trigonometric Functions
- Chapter 3: Matrices
- Chapter 4: Determinants
- Chapter 5: Continuity and Differentiability
- Chapter 6: Applications of Derivatives
- Chapter 7: Integrals
- Chapter 8: Applications of Integrals
- Chapter 9: Differential Equations
- Chapter 10: Vector Algebra
- Chapter 11: Three-Dimensional Geometry
- Chapter 12: Linear Programming
- Chapter 13: Probability
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