One to One (Injective) function
A function f: X → Y is said to be a one-to-one function if the images of distinct elements of X under f are distinct. Thus, f is one to one if f(x1) = f(x2)
Property: A function f: A → B is one-to-one if f(x1) = f(x2) implies x1 = x2, i.e, an image of a distinct element of A under f mapping (function) is distinct.
Condition to be One-to-One function: Every element of the domain has a single image with a codomain after mapping.
Read More about One-to-One Functions.
Examples of One to One Functions
Som of examples of one-one functions are:
- f(x) = x (Identity function)
- k(x) = 2x + 3 (Linear Polynomial)
- g(x) = ex (Exponential function)
- h(x) = √x (Square root function, defined for x ≥ 0)
Types of Functions
Functions are defined as the relations which give a particular output for a particular input value. A function has a domain and codomain (range). f(x) usually denotes a function where x is the input of the function. In general, a function is written as y = f(x).
Table of Content
- What is a Function?
- Types of Functions in Maths
- One to One (Injective) function
- Many to One function
- Onto (Surjective) Function
- Into Function
- Summary: Types of Functions