How do you find an inverse?
Swap x and y in y = f(x), then solve for y.
Inverse Function Calculator
Solve for x in terms of y to get f⁻¹ for linear or simple reciprocal functions.
Choose a function type
Select y = ax+b or y = a/x and enter coefficients.
About this calculator
How to use Inverse Function Calculator, plus the formulas and logic behind the results.
Tool description
An inverse undoes a function: f(f⁻¹(x)) = x on the appropriate domain. Linear functions need a ≠ 0; y = a/x needs a ≠ 0.
How to use
- Select linear or reciprocal form.
- Enter a (and b for linear).
- Select Calculate to view f⁻¹(x).
- Check domain notes in the results.
Formulas & reference
If y = ax + b (a ≠ 0), then x = (y − b)/a → f⁻¹(x) = (x − b)/aIf y = a/x (a ≠ 0), then x = a/y → f⁻¹(x) = a/x (same form)
Checks
- y = 2x+3 → f⁻¹(x) = (x−3)/2
- y = 5/x → f⁻¹(x) = 5/x
- Swap x and y, then solve for y
- Verify with f(f⁻¹(x)) = x
Calculation logic
Inverts algebraically for the selected form and rejects non-invertible cases (a = 0).
Constant functions (a = 0 in linear mode) are not invertible.
Inverse Function Calculator FAQ
Common questions about this calculator and how to use the results.
When is a linear function invertible?
When the slope a is not zero.
Is y = a/x its own inverse?
Yes when a ≠ 0: applying twice returns x (for x ≠ 0).
What about restricted domains?
Inverses need one-to-one behavior; this tool uses globally invertible forms.
Do inverses reverse domain and range?
Yes—the range of f becomes the domain of f⁻¹.
Why reject a = 0?
A constant linear function maps many x to one y, so no inverse function exists.