Topics
Relations and Functions
- Fundamental Concepts of Ordered Pairs and Relations
- Types of Relations
- Equivalence Class and Relation
- Congruence Modulo
- Domain and Range of a Function
- Real-Valued and Real Functions
- Types of Functions
- Composition of Functions
- Invertible Functions
- Binary Operations
- Overview of Relations and Functions
Section A
Inverse Trigonometric Functions
- Meaning and Interpretation of Inverse Trigonometric Functions
- Principal Values of Inverse Trigonometric Functions
- Graphs and Domains & Ranges of Inverse Trigonometric Functions
- Properties of Inverse Trigonometric Functions
- Overview of Inverse Trigonometric Functions
Section B
Matrices
Section C
Determinants
Continuity and Differentiability
Indeterminate Forms
Applications of Derivatives
Integrals
Differential Equations
Probability
Vectors
Three Dimensional Geometry
Applications of Integrals
Application of Calculus in Commerce and Economics
Linear Regression
Linear Programming
Estimated time: 1 minutes
- Composition of three functions
Maharashtra State Board: Class 12
Definition: Composition of Functions
Let f: A → B and g: B → C be any two functions. Then, the composition of f and g, denoted by gof, is defined as a function gof: A → C given by
gof(x) = g[f(x)], ∀ x ∈ A
- Domain (gof) = Domain (f)
- g∘f(x) = g(f(x)) → first apply f, then g
