Domain Calculator
Estimate the domain of f(x) by sampling the expression parser across a wide range of x values.
About Domain Calculator
This calculator estimates the domain of f(x) by evaluating the expression at many evenly-spaced sample points and identifying where the function produces finite results. It detects regions where the function is undefined (e.g., square roots of negatives, division by zero, logarithms of non-positive values).
Formula
Sampling approach
Evaluate f(x) at 2001 evenly-spaced points in [lo, hi] and identify where f(x) is defined
- lo
- Lower bound of search range
- hi
- Upper bound of search range
Worked example
With the default values below, Domain Calculator returns Estimated Domain of Approximately [2, 100]. Change any input above and every figure here is recalculated in your browser.
Inputs used
- f(x)
- sqrt(x - 2)
- Search range lower
- -100
- Search range upper
- 100
Results
- Estimated Domain
- Approximately [2, 100]
- Defined sample points
- 981
- Total sample points
- 2,001
Step by step
- 1Values used
- 2Sampling approach
- 3Estimated Domain= Approximately [2, 100]
- 4Defined sample points= 981
- 5Total sample points= 2,001
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Is this an exact domain calculation?
No — it is a numerical estimate based on sampling. It may miss isolated undefined points or boundaries between very close sample points.
How can I improve accuracy?
Narrow the search range around the region of interest. The 2001 sample points will then be more densely packed.