Inverse Function Calculator
Numerically approximate f⁻¹(y) by finding x where f(x)=y using bisection search.
Inputs
Must be monotonic on the search interval
f⁻¹(y) ≈ x
2.00000000
f(x) at solution
10.00000000
Bisection iterations
48
Step by step
Values used
f(x) = x^3 + x; y (target value) = 10; Search interval lower bound = -100; Search interval upper bound = 100
Bisection method
Repeat: mid = (lo+hi)/2; if f(mid)-y has same sign as f(lo)-y then lo=mid, else hi=mid
f⁻¹(y) ≈ x
= 2.00000000
f(x) at solution
= 10.00000000
Bisection iterations
= 48
How it works
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
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.