Inverse Function Calculator
Numerically approximate f⁻¹(y) by finding x where f(x)=y using bisection search.
About Inverse Function Calculator
This calculator numerically finds x such that f(x) = y using the bisection method. The function must be continuous and the interval [lo, hi] must bracket the solution (f(lo)−y and f(hi)−y must have opposite signs). The method converges to machine precision in about 50 iterations.
Formula
Bisection method
Repeat: mid = (lo+hi)/2; if f(mid)-y has same sign as f(lo)-y then lo=mid, else hi=mid
- lo
- Lower bound
- hi
- Upper bound
- y
- Target value
Worked example
With the default values below, Inverse Function Calculator returns f⁻¹(y) ≈ x of 2.00000000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- f(x)
- x^3 + x
- y (target value)
- 10
- Search interval lower bound
- -100
- Search interval upper bound
- 100
Results
- f⁻¹(y) ≈ x
- 2.00000000
- f(x) at solution
- 10.00000000
- Bisection iterations
- 48
Step by step
- 1Values used
- 2Bisection method
- 3f⁻¹(y) ≈ x= 2.00000000
- 4f(x) at solution= 10.00000000
- 5Bisection iterations= 48
Assumptions and limits
- The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
What if the function is not monotonic?
Bisection requires a sign change. If the function is not monotonic on the interval, narrow the interval to a region where it is.
How accurate is the result?
The bisection method converges to approximately 12 decimal places of precision within 100 iterations.