Analyze domain rules for roots, fractions, and logs. Get intervals, exclusions, steps, and quick exports. Use structured inputs to reduce algebra mistakes every time.
Fraction rule: If an expression is in a denominator, then denominator ≠ 0.
Even root rule: If an expression is inside an even root, then radicand ≥ 0.
Log rule: If an expression is inside a logarithm, then argument > 0.
Log base rule: Base > 0 and base ≠ 1.
Manual bound: Apply x > k, x ≥ k, x < k, x ≤ k, or x ≠ k.
Final domain: Intersect all valid sets.
Domain = D₁ ∩ D₂ ∩ D₃ ∩ D₄
| Denominator | Root Radicand | Log Argument | Manual Bound | Final Domain |
|---|---|---|---|---|
| -x² + 9 ≠ 0 | x² - 4x + 3 ≥ 0 | Disabled | x ≥ 0 | [0, 1] ∪ (3, ∞) |
| x - 2 ≠ 0 | Disabled | x + 5 > 0 | x < 10 | (-5, 2) ∪ (2, 10) |
A domain inequality calculator helps you find every valid input for an expression. That matters in algebra, precalculus, and calculus. Many expressions look simple but hide restrictions. A denominator cannot be zero. A square root needs a nonnegative radicand. A logarithm needs a positive argument. This page combines those rules in one workflow.
You can activate fraction, root, logarithm, and manual boundary conditions. Then you enter coefficients for each expression. The tool builds the matching inequality rule. Next, it solves each restriction and intersects all allowed sets. That gives the final domain in interval notation. It also lists each active condition, so you can verify the logic.
Domain restrictions protect you from undefined values. They also improve graphing, equation solving, and model building. If you ignore restrictions, you may accept impossible answers. In advanced problems, several rules can apply at once. A rational expression may also sit inside a root or logarithm. Intersections become the key idea.
The calculator evaluates linear and quadratic expressions. It finds critical points from roots and sign changes. Then it tests the needed rule, such as greater than zero, greater than or equal to zero, or not equal to zero. After that, it merges the valid intervals. The result is easier to read and export.
Use this tool for homework checks, lesson planning, exam review, or quick verification during algebra practice. It is useful for expressions involving radicals, rational terms, and logarithmic conditions. The example table also shows how multiple restrictions interact. That makes the calculator practical for both beginners and advanced learners.
Do not confuse the expression domain with the inequality solution unless the problem asks for both. A root rule uses a closed condition. A log rule uses an open condition. A denominator uses exclusion points only. Watch repeated roots carefully as well. They can change endpoint behavior without changing the sign on both sides. This calculator highlights those details, so your interval answer stays consistent and accurate.
It also supports quick CSV and PDF exports for record keeping and classroom review.
It returns the valid x values for the selected expression rules. The final answer appears in interval notation. It also shows each restriction separately.
Yes. Enable only the denominator section. Enter the coefficients, submit the form, and the tool will exclude values that make the denominator zero.
An even root requires a nonnegative radicand in real-number algebra. That is why the calculator uses a closed inequality for root restrictions.
A logarithm is defined only for positive arguments. Zero is not allowed. Negative values are also invalid in the real-number system.
Yes. It intersects every active set. That helps with expressions containing fractions, radicals, logs, and extra x bounds at the same time.
Yes. Each restriction section accepts coefficients for a linear or quadratic expression. Constant cases also work because the same solver logic handles them.
An empty set means the selected restrictions conflict. No real x value satisfies every active rule together.
Yes. After calculation, use the CSV or PDF buttons. They export the final domain and the detailed restriction table.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.