Full swap-and-solve.
Variable swap, then every algebra step needed to isolate the new y, shown with operation names.
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AI Solver by AskSia
Inverse of a Function Solver: every step shown
Paste your function or snap a picture. AskSia writes y = f(x), swaps the variables, solves the new equation, restricts the domain if the original is not one-to-one, and verifies the result by composing f with f^(-1). Both graphs appear together with the line y = x for visual confirmation.
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
What is the inverse of a function?
The inverse of a function f, written f^(-1), is the function that undoes f. If f(a) = b, then f^(-1)(b) = a. To find it, write y = f(x), swap x and y to get x = f(y), and solve for y. The original must be one-to-one for the inverse to be a function; otherwise restrict the domain. Verify by composing: f(f^(-1)(x)) = x and f^(-1)(f(x)) = x.
98%
solution accuracy
50M+
problems solved
~1.5s
avg solve time
A+
study-ready explanations
Why AskSia Solver
Built for the moments when 'just swap x and y' is not enough.
Every algebra move shown, every restriction stated, every check performed.
Domain restriction logic.
When a function fails the horizontal line test, AskSia picks a largest interval where it is monotonic and reports the restriction explicitly.
Smart
Composition verification.
f(f^(-1)(x)) gets simplified back to x as proof the inverse is correct. Any non-simplification gets flagged.
Verified
Range and domain swap.
AskSia computes the domain and range of f, then swaps them to state the domain and range of f^(-1).
Complete
Graph with reflection.
Both functions plotted on one axes with y = x drawn, making the symmetry visible.
Visual
Multi-modal input.
Type the function, paste it, take a photo, or say it out loud. AskSia parses every standard form.
Multi-modal
How It Works
Three steps to the inverse.
Step 01
Enter the function.
Type f(x), paste from class notes, snap a picture, or speak the expression. AskSia parses 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
Swap and solve.
y = f(x), then x = f(y). AskSia performs every operation needed to isolate y on one side.
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
Verify and graph.
Composition of f and f^(-1) is checked. Domain and range of f^(-1) are stated. Both functions are 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
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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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Calc
98%
1.4s
Area between y=2x & y=x²
A = 4/3 sq. units ✓
Use Cases
Where inverse functions show up.
Linear functions.
f(x) = ax + b inverts to f^(-1)(x) = (x-b)/a. AskSia still walks through the swap-and-solve so the method generalizes.
Algebra 1
Quadratic with restricted domain.
f(x) = x^2 for x >= 0 inverts to f^(-1)(x) = sqrt(x). AskSia handles the restriction.
Algebra 2
Rational and radical.
f(x) = (2x+1)/(x-3) and f(x) = sqrt(x+4) - 2. Standard inverse-finding problems with multi-step algebra.
Pre-Calc
Exponential and log.
f(x) = e^x and f(x) = ln(x) are inverses. AskSia shows the change of variable explicitly.
Logs
Trig functions on restricted domain.
Arcsin, arccos, arctan with the standard conventional ranges. AskSia states the convention used.
Trig
Word problems.
If f tells you the cost from quantity, f^(-1) tells you quantity from cost. AskSia applies the inverse-finding method in context.
Applications
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 does the function need to be one-to-one?
If two different inputs give the same output, the inverse cannot decide which input to return when fed that output, so the inverse fails to be a function. AskSia tests one-to-oneness by analyzing the function's behavior (monotonicity, horizontal line test) and restricts the domain when the original is not one-to-one over its full domain.
What is the difference between f^(-1)(x) and 1/f(x)?
Completely different. f^(-1) is the inverse function (the undo of f), while 1/f is the reciprocal of the function (one divided by f's output). The notation looks similar but the meaning is unrelated. AskSia always interprets f^(-1) as inverse, not reciprocal, and labels the result accordingly to avoid confusion.
How is the inverse of an exponential function found?
Write y = b^x, swap to get x = b^y, then take a logarithm with base b on both sides: log_b(x) = y. So the inverse of b^x is log_b(x). AskSia shows the logarithm step explicitly and lists the resulting domain (positive reals) and range (all reals) for the inverse.
Can the inverse be drawn as a reflection?
Yes. The graph of f^(-1) is the reflection of the graph of f across the line y = x. AskSia produces both graphs on the same axes with that diagonal line drawn, so you can see the reflection symmetry as a visual confirmation of the inverse calculation.
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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Join 2M+ students using AskSia to compute inverse functions with every step shown, every restriction stated, and a reflection graph on every solve.
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