Finding Inverses Calculator
Finding inverses calculator works out f-inverse(y) and Inverse function from f(x) =, Variable and Output value y to invert. The default figures on this page give f-inverse(y) of 4; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
5 steps
- Start from y = 2 * x + 3.
- Swap the roles of x and y, then undo each operation in reverse order.
- f-inverse(x) = (x - 3) / 2.
- Substituting x = 11 gives f-inverse(11) = 4.
- Check: f(4) = 11 (target 11).
Points on f and on f-inversetable
| x | f(x) | inverse point x | inverse point y |
|---|---|---|---|
| -33.333333 | -63.666667 | -63.666667 | -33.333333 |
| -16.666667 | -30.333333 | -30.333333 | -16.666667 |
| 0 | 3 | 3 | 0 |
| 16.666667 | 36.333333 | 36.333333 | 16.666667 |
| 33.333333 | 69.666667 | 69.666667 | 33.333333 |
Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
3 sources
What the finding inverses calculator calculates
Finds the inverse of a function by undoing its operations in reverse order, evaluates the inverse at a chosen output value, and checks whether the function is one-to-one on the given interval.
How to use this finding inverses calculator
Enter f(x) =, Variable, Output value y to invert and Search from x =. F-inverse(y) updates as you type, and “Use a worked example” loads checked figures you can adjust. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind f-inverse(y), Inverse function and Method used.
The method follows OpenStax College Algebra, section 3.7 "Inverse Functions", Stewart, Redlin & Watson, Precalculus: Mathematics for Calculus, section on one-to-one functions and their inverses and Burden & Faires, Numerical Analysis, section 2.1 (the bisection method).
f(x) = 2x + 3 at y = 11 example
With f(x) =: 2x + 3, Output value y to invert: 11, the calculator returns f-inverse(y): 4, Check: f applied to the answer: 11, Method used: symbolic. This example is checked against an independent source in the test suite.
What you can compare
Change one input at a time to see how it affects f-inverse(y), Inverse function and Method used. The inputs you can vary are f(x) =, Variable, Output value y to invert, Search from x =, Search to x = and Table rows.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
How to find inverse with calculator?
Finds the inverse of a function by undoing its operations in reverse order, evaluates the inverse at a chosen output value, and checks whether the function is one-to-one on the given interval. Open “How this is worked out” beside the result to see each step for your own figures.
How to find inverse on TI-84 calculator?
It needs f(x) =, Variable, Output value y to invert, Search from x =, Search to x = and Table rows. Nothing else is required, and the figures stay in your browser.
How do I find inverses?
The result gives f-inverse(y), Inverse function, Method used, Check: f applied to the answer, One-to-one on the interval and Domain and branch notes, each labelled with its unit so the figure can be read on its own.
What is the inverse of y =- 2x + 3?
On the figures this page opens with — output value y to invert 11 — the f-inverse(y) is 4. No single number fits everyone: change any figure above and the answer updates as you type, with each step of the arithmetic beside it.
What information do I need for the finding inverses calculator?
You need f(x) =, Variable, Output value y to invert, Search from x =, Search to x = and Table rows. The page opens with default figures that give f-inverse(y) of 4, so you can see the scale before entering your own.
What does this finding inverses calculator show?
It shows f-inverse(y), Inverse function, Method used, Check: f applied to the answer, One-to-one on the interval, Domain and branch notes, Points on f and on f-inverse and Verification residual, with the working and any warnings for your entries.