Every breaker checked.
Denominator zeros, negative radicands, non-positive log arguments. AskSia tests each restriction and produces the excluded set.
Complete
AI Solver by AskSia
Domain Solver: where the function is defined
Paste any function or snap a photo. AskSia checks every place the function can fail (denominator zeros, negative radicands, log arguments at or below zero, composition constraints) and gives you the domain in interval notation with every excluded value explained.
Works with word problems, equations, code, and science prompts.
∫ 3x² · sin(x) dx
SubjectsCalculusAlgebraPhysicsChemistryBiologyCSStatisticsEcon
4.9 / 5 · trusted by 2M+ students · 50M+ problems solved
asksia.ai/solver
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Problem
Find the area enclosed between y = x² and y = 2x in the first quadrant.
1
Find the points of intersection
Set the curves equal: x² = 2x → x(x - 2) = 0, so x = 0 and x = 2.
2
Identify which curve is on top
On (0, 2), 2x > x², so y = 2x is the upper curve.
3
Set up the area integral
A = ∫₀² (2x - x²) dx
4
Integrate term-by-term
A = [ x² - x³/3 ]₀²
Final Answer
A = 4/3 sq. units
Quick Answer
What is the domain of a function?
The domain of a function is the set of input values for which the function produces a real output. To find it, list every place the function could break: denominators cannot equal zero, even-root radicands cannot be negative, and log arguments must be strictly positive. For composed functions, the inner output must lie in the outer's domain. The domain is then everything not excluded, typically written in interval notation as a union of intervals on the real line.
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solution accuracy
50M+
problems solved
~1.5s
avg solve time
A+
study-ready explanations
Why AskSia Solver
Why students use AskSia for domain analysis.
Every restriction caught, every exclusion explained.
Composition restrictions.
For f(g(x)), the domain is the set of x in g's domain such that g(x) lies in f's domain. AskSia tracks both conditions.
Composition
Interval notation default.
Answer appears as a union of intervals. Set-builder available on toggle for more complex restrictions.
Standard form
Excluded values listed.
Every value or set excluded gets named with the algebraic reason (denominator zero at x=2, log undefined for x<=0).
Transparent
Graph included.
The function plot highlights the domain on the x-axis, with breaks at vertical asymptotes and open dots at holes.
Visual
Piecewise handled.
For piecewise definitions, AskSia analyzes each piece and combines into a single domain description.
Piecewise
How It Works
Find any domain in three steps.
Step 01
Enter f(x).
Type, paste, photograph, or speak the function. AskSia identifies its type and the places it could be undefined.
Input mode
Snap a Photo
Textbook, handwriting, screenshot
Paste Text
Word problem or equation
Calculator
LaTeX-ready equation editor
Step 02
AskSia checks restrictions.
Denominators are set to zero and solved. Radicands and log arguments get sign analysis. Composition outputs are constrained.
1
Set curves equal
x² = 2x → x = 0, x = 2
2
Set up the integral
A = ∫₀² (2x - x²) dx
3
Evaluate
A = [x² - x³/3]₀² = 4/3
Step 03
Read the domain.
Final domain in interval notation, list of excluded values with reasons, and a graph highlighting the defined region on the x-axis.
Auto-generated diagram
Region between y = 2x and y = x² — area = 4/3
Available On
Solve anywhere
you study.
Every solve syncs across Web, iOS, and Android — start it at your desk, finish on your phone.
Web App
Full study studio
Split-panel interface with the worked solution on the left, the auto-generated diagram and AI tutor chat on the right.
Drag & drop image upload + LaTeX equation editor
Auto-generated diagrams render alongside steps
Side-panel AI tutor chat for hints and alt methods
Export to PDF, DOCX, Notion, or Google Docs
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Calculus
98% verified
1.4s
Step 4 of 4 · Evaluate
A = [x² - x³/3]₀² = 4/3
Mobile App
Snap & solve, anywhere
Open the camera, frame the problem, and the worked solution plus diagram appear in seconds.
One-tap snap-and-solve on iOS and Android
Pinch-to-zoom diagrams, swipe between steps
Auto-sync solves with your Web library
Offline review of saved solutions and flashcards
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1.4s
Area between y=2x & y=x²
A = 4/3 sq. units ✓
Use Cases
Domain analysis across the curriculum.
Rational functions.
Set the denominator equal to zero and exclude those x-values. AskSia factors and lists each excluded point.
Rational
Square root and radicals.
Set the radicand >= 0 (for even roots) and solve the inequality to get the domain.
Radical
Logarithms.
Set the argument > 0 and solve the inequality. AskSia handles natural log, log base 10, and any other base.
Logs
Composite functions.
f(g(x)) restrictions come from both f and g. AskSia chains the constraints carefully.
Composition
Real-world models.
A function modeling speed, cost, or population may have a practical domain (e.g. time >= 0) on top of the algebraic domain.
Applications
Verify a stated domain.
Paste a function and a proposed domain. AskSia checks every claimed exclusion and tells you if any are missing.
Check
Compare
AskSia vs. ChatGPT,
Photomath & Symbolab.
General chatbots hallucinate. Photo solvers stop at math. AskSia is built for actual coursework with verified accuracy, visual learning, and every subject.
| Feature | AskSia Solver | ChatGPT | Photo Solvers |
|---|---|---|---|
| Solution accuracy | ✓ 98% | ~70-85%, hallucinations | ~90%, math only |
| Auto-generated diagrams | ✓ Every solve | Inconsistent / broken | Graphs only, math-only |
| Step-by-step explanations | ✓ Numbered + plain English | Inconsistent depth | ✓ Math steps |
| Subject coverage | ✓ Math, Physics, Chem, Bio, CS, Econ | ✓ Wide but unverified | Math only |
| Photo input | ✓ Handwriting + diagrams + code | Photos OK, weak on handwriting | ✓ Math photos only |
| Answer verification | ✓ Self-checked before display | No verification | Math engine only |
| Tutor follow-ups | ✓ Hints, alt methods, ELI5 | ✓ General chat | Not available |
| Practice and flashcards | ✓ One-tap from any solve | Manual prompting | Not available |
| Code debugging | ✓ Python, Java, C++, SQL... | ✓ Yes | Not available |
| Free to start | ✓ Daily solves, no card | Limited model access | Steps locked behind paywall |
FAQ
Frequently asked questions.
Why are denominator zeros excluded?
Division by zero is undefined. If a function has a denominator and that denominator equals zero for some input, the function has no value there and that input must be excluded from the domain. AskSia sets the denominator equal to zero, solves the equation, and excludes every solution from the domain.
What about square roots of negative numbers?
Over the real numbers, even-root radicals require non-negative radicands. AskSia sets the radicand >= 0, solves the resulting inequality, and intersects with any other restrictions to find the domain. Odd-root radicals (like cube roots) have no such restriction and accept all real inputs.
How are logarithm domains determined?
The argument of a logarithm must be strictly positive (greater than zero, not equal to zero). AskSia sets the log argument > 0 and solves the inequality. For composite logs like log(g(x)), this gives a condition on x that joins any other restrictions from g.
What is the domain of a composition f(g(x))?
Two conditions: x must be in the domain of g (so g(x) is defined), and g(x) must be in the domain of f (so f can evaluate it). AskSia computes both conditions and intersects them. The result can be smaller than the domain of either f or g alone.
How accurate is AskSia?
AskSia is engineered for accuracy on standard high school and college coursework. Accuracy comes from subject-specialized models, a symbolic verification pass that catches arithmetic errors, and a self-check step that re-derives the answer before showing it to you.
Can I get practice problems and flashcards?
Yes. After any solve, ask Sia to generate similar practice problems at SAT, ACT, AP, IB, or college difficulty, or build a flashcard set on the underlying concept in one tap. Useful for exam prep and spaced repetition before a quiz, midterm, or final.
How much does AskSia cost?
AskSia has a free plan that includes daily solves across all subjects. AskSia Pro and Super include unlimited solves, advanced subjects, the full AI tutor companion, exports, and priority response speed. See pricing for details.
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Every excluded value, every restriction, clearly stated.
Join 2M+ students using AskSia to find function domains with full step-by-step analysis. Interval notation, excluded values explained, and a graph on every solve.
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