Function Inverse Calculator
Enter a function of x and get its inverse f⁻¹(x). The calculator detects the structural pattern of the input — linear, linear-fractional, square root, exponential, logarithmic or quadratic — and returns the inverse together with any domain restrictions implied by that pattern.
Frequently asked questions
Which functions can be inverted?
Linear (mx + b), linear-fractional ((ax + b)/(cx + d)), square root of a linear, exp(linear), ln(linear) and quadratic on a restricted domain. Other patterns return a clear error.
Why does the quadratic inverse mention 'principal branch'?
A function like y = x² is not one-to-one on all of ℝ, so it does not have a single inverse. The calculator returns the inverse on the standard right branch (x ≥ vertex), which is the convention used in textbooks.
Does it handle trigonometric inverses?
Not in v1 — use the dedicated trig tools for arcsin / arccos / arctan instead. Symbolic trig inversion has its own conventions about principal value ranges.