Example Data Table
| Function | Main restriction | Domain | Reason |
|---|---|---|---|
| sqrt(x - 2) | x - 2 ≥ 0 | [2, ∞) | Square root needs a nonnegative radicand. |
| 1 / (x - 3) | x - 3 ≠ 0 | (-∞, 3) ∪ (3, ∞) | Division by zero is not allowed. |
| log(x + 4) | x + 4 > 0 | (-4, ∞) | Logarithm needs a positive argument. |
| asin(x / 5) | -1 ≤ x / 5 ≤ 1 | [-5, 5] | Inverse sine accepts inputs from -1 to 1. |
Formula Used
The calculator uses domain restriction rules and numerical testing. It intersects every detected rule.
- For fractions, denominator ≠ 0.
- For square roots and even roots, radicand ≥ 0.
- For logarithms, argument > 0.
- For asin(u) and acos(u), -1 ≤ u ≤ 1.
- For combined functions, final domain = rule one ∩ rule two ∩ all remaining rules.
How to Use This Calculator
- Enter your function in the function field.
- Use x unless you choose another single-letter variable.
- Set a minimum and maximum x range for testing.
- Use a smaller step for finer numerical checks.
- Press Calculate Domain to view the result above the form.
- Use CSV or PDF buttons to download the current calculation.
Domain Finder Guide
A function accepts only certain input values. These values form its domain. Many classroom problems hide limits inside common operations. A denominator cannot become zero. An even root cannot use a negative radicand. A logarithm must receive a positive argument. Inverse sine and inverse cosine need inputs from negative one to one. This calculator checks those ideas together.
Why Domain Matters
Domain tells you where a formula makes sense. It protects graphs from impossible points. It also helps before solving equations. When the domain is known first, extra answers become easier to reject. This is useful in algebra, calculus, modeling, and test preparation.
How The Tool Works
Enter a function using x as the variable. You may use powers, fractions, square roots, logarithms, trigonometric functions, and inverse trigonometric functions. The tool reads visible restrictions and tests values across your selected range. It then reports allowed intervals, excluded points, sample outputs, and notes. The result is numerical, so use the explanation beside it for final proof.
Common Restrictions
Fractions are checked first because zero denominators break division. Radical expressions are checked next. For a square root, the radicand must be zero or positive. Logarithmic expressions are stricter. Their arguments must be greater than zero. Inverse trigonometric rules are also tested. These restrictions combine by intersection. A value must satisfy every condition at once.
Reading The Result
The interval line shows the estimated domain inside your chosen scan limits. Brackets mean an endpoint appears allowed. Parentheses mean it is excluded or outside the tested range. The restrictions list explains why points were removed. The sample table shows how nearby inputs behave. This helps you spot holes, endpoints, and continuous regions.
Best Practice
Use a wide scan range for broad graphs. Use a smaller step for more detail. Type multiplication with an asterisk when needed. Write 2*x instead of 2x for safest reading. Compare the output with the formulas shown below. For exact coursework, turn each restriction into an inequality, solve it, and intersect the answers carefully.
Keep entries simple during checks. Start with one expression. Then add extra terms gradually. This habit finds typing mistakes early. It also makes each restriction easier to understand and verify later manually.
FAQs
What is the domain of a function?
The domain is the set of input values that make a function real and defined. It excludes values causing zero denominators, negative even roots, invalid logs, or other impossible operations.
Can this calculator find exact domains?
It gives strong numerical guidance and lists algebraic restrictions. For exact work, solve each listed inequality or exclusion by hand, then intersect the results.
Which functions are supported?
You can use powers, fractions, sqrt, cbrt, root, log, ln, log10, abs, trig functions, inverse trig functions, exp, min, and max.
How should I type powers?
Use the caret symbol. For example, type x^2 for x squared. Parentheses help avoid confusion, such as (x+1)^2.
Why does the result mention a selected range?
The tool tests real values between your minimum and maximum x. Increase the range when you want to inspect wider behavior.
Why is my interval only an estimate?
Numerical scanning checks many points and likely boundaries. Very narrow gaps may need smaller steps or exact algebraic solving.
Can I export my work?
Yes. Use the CSV button for spreadsheet data. Use the PDF button for a simple printable summary of the current result.
Does it support inverse trigonometric restrictions?
Yes. It checks asin and acos inputs against the interval from negative one to one. Those limits are included when valid.