Variable swap shown.
y = f(x) becomes x = f(y) in one labeled step, so the conceptual move is never hidden.
Conceptual
LMS Integration
Uni & Course Analysis
Useful Tools
Resources
EN
Inverse Function Solver
Any function. Inverted, restricted, verified.
Type f(x) or snap it from your homework. AskSia rewrites y = f(x), swaps x and y, solves for the new y, and gives you f^(-1)(x). When the original is not one-to-one (like a quadratic over its full domain), AskSia restricts the domain so the inverse exists, and then verifies the result by composing f and f^(-1).
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
98% · Verified
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
How do you find the inverse of a function?
To find the inverse of f(x), write y = f(x), then swap x and y to get x = f(y). Solve this new equation for y in terms of x, and that expression is f^(-1)(x). The function must be one-to-one (each output comes from exactly one input) for the inverse to be a function; if it is not, restrict the domain first. Verify by composing: f(f^(-1)(x)) should simplify to x, and so should f^(-1)(f(x)).
98%
solution accuracy
50M+
problems solved
~1.5s
avg solve time
A+
study-ready explanations
Why AskSia Solver
Why students use AskSia to find inverses.
Swap, solve, restrict, verify. Each step explicit.
Solving made transparent.
Whatever the algebra requires (factoring, square roots, logarithms, isolation), AskSia shows every operation as it solves for the new y.
Step-by-step
Domain restriction handled.
If the original is not one-to-one, AskSia restricts to the largest interval where it is, and reports that restriction clearly.
Smart
Composition verification.
f(f^(-1)(x)) gets composed and simplified back to x as a check. If it does not collapse, AskSia flags the issue.
Verified
Graph included.
f and f^(-1) appear on the same axes along with the line y = x, so the reflection symmetry is visible at a glance.
Visual
Domain and range tracked.
The domain of f becomes the range of f^(-1) and vice versa. AskSia states both and shows the swap.
Domain-aware
How It Works
Find any inverse in three steps.
Step 01
Enter f(x).
Type, paste, photograph, or speak the function. AskSia identifies the function type and checks one-to-oneness.
Input mode
Snap a Photo
Textbook, handwriting, screenshot
Paste Text
Word problem or equation
Calculator
LaTeX-ready equation editor
Step 02
AskSia swaps and solves.
Write y = f(x), swap x and y, solve for y in terms of x. Each algebraic step is labeled.
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 f^(-1)(x) and the check.
The inverse is stated with its domain and range, composition verifies it equals x, and both functions get graphed with y = x.
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
Hi! What are we studying today?
Ask about your homework, lecture, or readings...↑
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
☰
AskSia
+What can I do for you?
Homework solver
Live transcribe
File summary
Snap
YouTube
Flashcard
Calc
98%
1.4s
Area between y=2x & y=x²
A = 4/3 sq. units ✓
Use Cases
What the inverse function solver covers.
Linear inverses.
f(x) = 3x - 7 inverts trivially. AskSia still shows the swap-and-solve so the pattern sticks.
Algebra 1
Quadratic inverses with restriction.
f(x) = x^2 needs a domain restriction. AskSia picks x >= 0 (or the side you specify), inverts, and reports the restricted domain.
Algebra 2
Rational and radical inverses.
f(x) = (x+1)/(x-2), f(x) = sqrt(x-3), and similar. AskSia clears fractions or squares as needed.
Pre-Calc
Exponential and logarithmic.
The inverse of e^x is ln x, and AskSia shows the logarithm step explicitly so the relationship is clear.
Logs
Trigonometric inverses.
On restricted domains, sin, cos, and tan have inverses (arcsin, arccos, arctan). AskSia states the conventional restrictions.
Trig
Verify a candidate inverse.
Paste a function and a proposed inverse. AskSia composes them and tells you whether the composition equals x.
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.
When does a function not have an inverse?
A function has an inverse only when it is one-to-one, meaning each output value comes from exactly one input. f(x) = x^2 is not one-to-one over all reals because f(2) = f(-2) = 4. AskSia tests one-to-oneness by checking the horizontal line test analytically, and if the function fails, it restricts the domain to the largest interval where the function is monotonic so an inverse exists there.
How does the composition check work?
After finding f^(-1)(x), AskSia computes f(f^(-1)(x)) by substituting f^(-1)(x) into f and simplifying algebraically. The result should reduce to x. If it does not, the inverse calculation contains an error and AskSia flags which step likely went wrong.
What are the domain and range of the inverse?
Swap. The domain of f^(-1) is the range of f, and the range of f^(-1) is the domain of f. AskSia computes both for the original function (with domain restriction if needed) and states the corresponding domain and range of the inverse alongside f^(-1)(x).
Can AskSia graph the original and the inverse together?
Yes. Both appear on the same axes with the line y = x drawn for reference, so you can see that the graphs are mirror images across y = x. This visualization makes the reflection property of inverse functions concrete instead of abstract.
How accurate is AskSia?
AskSia hits 98% accuracy on standard high school and college coursework, measurably higher than ChatGPT, Photomath, and Symbolab on the same problem sets. 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.
Start Today
Swap, solve, verify, graph.
Join 2M+ students using AskSia to find inverse functions with full step-by-step work. Domain restriction, composition verification, and a graph of f and f^(-1) on every solve.
Let's Get in Touch
