Expert Reviewer: David Chen, CFA — Mathematics & Financial Modeling Specialist
Determining the domain of a function is the first step in mathematical analysis. Our Domain of Function Calculator helps you instantly find the set of all possible input values (x) for which a function is defined, ensuring your calculations are mathematically sound and avoiding errors like division by zero or negative square roots.
Domain of Function Calculator
Domain of Function Calculator Formula
Depending on the function type $f(x)$:
- Rational: $ax + b \neq 0$
- Radical: $ax + b \geq 0$
- Logarithmic: $ax + b > 0$
Source: Wolfram MathWorld – Domain, Khan Academy
Variables Explained
- Function Type: The mathematical category of the expression (e.g., Linear, Fractional).
- Coefficient (a): The multiplier for the variable $x$ in the term $ax + b$.
- Constant (b): The fixed value added or subtracted in the expression.
Related Calculators
What is a Domain of Function Calculator?
A Domain of Function Calculator is a specialized tool used to find the “input” values for which a specific mathematical function is valid. In mathematics, the domain is the set of all real numbers that, when plugged into the function, result in a real, defined number.
Calculating the domain is essential in calculus, engineering, and data science because it prevents “undefined” outcomes. For example, in a rational function, the denominator can never be zero. This calculator automates the process of solving these inequalities to provide interval notation results.
How to Calculate Domain (Example)
Let’s find the domain for $f(x) = \frac{1}{2x – 4}$:
- Identify the constraint: Since it’s a rational function, the denominator $2x – 4$ cannot be $0$.
- Set up the equation: $2x – 4 \neq 0$.
- Solve for $x$: $2x \neq 4$, therefore $x \neq 2$.
- Write in interval notation: $(-\infty, 2) \cup (2, \infty)$.
Frequently Asked Questions (FAQ)
What is the domain of all polynomial functions? Generally, the domain of a polynomial (like $x^2 + 5$) is always “All Real Numbers” $(-\infty, \infty)$.
Why can’t the denominator be zero? Dividing by zero is undefined in mathematics because there is no number that, when multiplied by zero, gives a non-zero result.
What is the difference between domain and range? The domain is the set of all possible input values ($x$), while the range is the set of all possible output values ($y$).
Does this calculator handle complex numbers? No, this calculator focuses on the “Real Domain,” which is standard for most algebra and calculus courses.