Functions

Functions explained with definitions, domain and range, types of functions, and simple examples to build strong mathematical understanding.

1.Definition of a Function
Meaning of a function as a special relation where every input has exactly one output, with simple explanations and examples.
2.Domain of a Function
Meaning of the domain of a function, how to identify valid inputs, and simple examples to understand the idea.
3.Codomain of a Function
Meaning of the codomain of a function, how it differs from range, and simple examples.
4.Range of a Function
Meaning of the range of a function and how to find actual outputs using formulas or ordered pairs.
5.Overview of Types of Functions
Simple overview of different types of functions based on input-output behaviour and special properties.
6.One-One (Injective) Function
Meaning of a one-one (injective) function, how to check injectivity, and simple examples.
7.Onto (Surjective) Function
Meaning of an onto (surjective) function, how to check surjectivity, and simple examples.
8.Bijective Function
Meaning of a bijective function, combining one-one and onto behaviour, with simple explanations and examples.
9.Constant Function
Meaning of a constant function, how outputs stay fixed regardless of inputs, with examples.
10.Identity Function
Meaning of the identity function, how it maps every element to itself, with simple examples and properties.
11.Polynomial Function
Meaning of a polynomial function, its form, degree, and common examples.
12.Rational Function
Meaning of a rational function, how it is formed as a ratio of polynomials, and basic examples and properties.
13.Algebraic Function
Meaning of an algebraic function, how it is built using algebraic operations, and simple examples.
14.Real-Valued Function
Meaning of a real-valued function, how its outputs are real numbers, with simple explanations and examples.
15.Vector-Valued Function
Meaning of a vector-valued function, how it outputs vectors instead of single numbers, with simple examples.
16.Composition of Functions
Meaning of composition of functions, how one function is applied after another, with clear steps and examples.
17.Inverse of a Function
Meaning of the inverse of a function, how to check if an inverse exists, and clear examples to understand the idea.