Domain Of Function Calculator
The Domain of Function Calculator helps you quickly determine the domain, restrictions, and correct interval notation for different types of mathematical functions.
Instead of manually solving inequalities or checking for undefined values, this calculator instantly provides accurate results for:
- Polynomial functions
- Rational functions
- Square root functions
- Logarithmic functions
- Fraction functions
Whether you’re studying algebra, precalculus, or reviewing for exams, this tool simplifies domain calculations.
What Is the Domain of a Function?
The domain of a function is the set of all possible input values (x-values) for which the function is defined.
In mathematics, certain operations restrict values, such as:
- Division by zero
- Even roots of negative numbers
- Logarithms of zero or negative numbers
The domain tells us exactly which values are allowed.
Function Types Supported by the Calculator
1. Polynomial Function
Polynomial functions have the simplest rule.
Domain: All real numbers
Restrictions: None
Interval Notation: (-∞, ∞)
Example:
f(x) = x² − 5x + 6
All real numbers are valid inputs.
2. Rational Function
A rational function contains a variable in the denominator.
Domain Rule: Denominator cannot equal zero.
Example:
f(x) = 1 / (x − 4)
Restriction:
x ≠ 4
Interval notation:
(-∞, 4) ∪ (4, ∞)
The calculator allows you to enter denominator zeros (comma separated) and automatically formats restrictions and interval notation.
3. Square Root Function
For square root functions, the radicand (expression inside √) must be:
Greater than or equal to zero.
Example:
f(x) = √(x − 3)
Solve:
x − 3 ≥ 0
x ≥ 3
Domain:
[3, ∞)
The calculator lets you enter the minimum radicand value and generates the correct domain instantly.
4. Logarithmic Function
For logarithmic functions, the argument must be:
Strictly greater than zero.
Example:
f(x) = log(x − 2)
Solve:
x − 2 > 0
x > 2
Domain:
(2, ∞)
The calculator automatically applies the strict inequality rule.
5. Fraction Function
Fraction functions exclude specific values that make the denominator zero.
You can manually enter excluded values such as:
0, 5, −3
The calculator then displays:
Restrictions:
x ≠ 0, x ≠ 5, x ≠ −3
Interval notation:
(-∞, ∞) \ {0, 5, −3}
How to Use the Domain Calculator
- Select the function type.
- Enter required values (if needed).
- Click Calculate.
- View:
- Function Type
- Domain
- Restrictions
- Interval Notation
Click Reset to start over.
Why Use This Domain of Function Calculator?
✔ Fast and accurate
✔ Automatically formats interval notation
✔ Prevents common domain mistakes
✔ Beginner-friendly
✔ Free and easy to use
This tool is ideal for:
- High school students
- College algebra learners
- Teachers
- Homework help
- Exam preparation
Common Domain Mistakes This Tool Prevents
- Forgetting to exclude denominator zeros
- Using ≥ instead of > for logarithms
- Forgetting square root restrictions
- Writing incorrect interval notation
- Missing multiple excluded values
The calculator ensures correct formatting every time.
Frequently Asked Questions
What is domain in math?
The set of all input values where a function is defined.
Do polynomial functions have restrictions?
No, their domain is all real numbers.
Why can’t the denominator be zero?
Division by zero is undefined.
Why must square roots be non-negative?
Because real square roots of negative numbers do not exist.
Why must logarithmic arguments be positive?
Logarithms of zero or negative numbers are undefined.
Does this calculator show interval notation?
Yes, it automatically generates correct interval notation.
Final Thoughts
The Domain of Function Calculator makes solving domain problems simple and accurate. Whether you’re working with rational expressions, square roots, logarithms, or polynomials, this tool gives you instant results with properly formatted restrictions and interval notation.
Use it to save time, avoid mistakes, and strengthen your understanding of function domains.