How to Find Domain and Range
Now to calculate the domain and range of any given function study the following example carefully:
For X = {1, 2, 3, 4, 5} and Y = {1, 2, 4, 5, …, 45, 46, 47, 48, 49, 50} and the function defined as f: X → Y, f(x) = x2 find the domain and range of the following function f(x)
Domain = All the input values = X
Range = {1, 4, 9, 16, 25} = A subset of Y
The domain of a function is the input value that we can take for a function and range of a function is the set of all the output values that the function achieves. Now domain and the range of the function is found using the example added below,
For example, if we are given a function F: X → Y, such that F(x) = y + 1, and X = {1, 2, 3, 4, 5} and Y = {1, 2, 3, 4, 5, 6}. Here,
- Domain of F(x) = X = {1, 2, 3, 4, 5}
- Range of F(x) = {2, 3, 4, 5, 6}
Y is the codomain of F(x) but not the range.
Domain and range of various types of functions are discussed in the next sections.
Domain and Range of a Function
Domain and Range of a Function: Domain and Range are the input and output values of a Function. A function is defined as the relation between a set of inputs and their outputs, where the input can have only one output i.e. a domain can yield a particular range. It depicts a relationship between an independent variable and a dependent variable.
A function is usually denoted by y = f(x), where x is the input. A function is a relation f from a set X to another set Y, where each element in X has exactly one output in Y, and it is represented as f: X→Y. Here the set X is known as the domain of a function, and the set Y is called the co-domain of the function. Every function has a domain, codomain, and range that help in defining the function.
In this article, we will learn about the domain and range of a function, how to calculate the domain and range of a function, the domain and range of a function worksheet, the domain and range of a function examples, domain and range of a function graph, and others in detail.
Table of Content
- What is Domain and Range?
- Interval Notation of Domain and Range
- Co-Domain and Range
- Domain of a Function
- How to Find the Domain of a Function?
- Range of a Function
- How to Find the Range of a Function?
- How to Find Domain and Range
- Domain and Range of a Function Examples
- Quadratic Domain and Range
- Domain and Range of Exponential Functions
- Domain and Range of Trigonometric Functions
- Domain and Range of Inverse Trigonometric Functions
- Domain and Range of an Absolute Value Function
- Domain and Range of a Square Root Function
- Domain and Range of a Rational Function
- Log Function Domain and Range
- Domain and Range of Greatest Integer Function
- Domain and Range of a Function Graph
- Domain and Range of a Function Worksheet
- Domain and Range Worksheet PDF
- Domain and Range Practice Problems
- Solved Questions on Domain and Range
Contact Us