Inverse Function Calculator
Find inverse functions f^(-1)(x) for common function types with verification.
Function Type
Inverse Function
f⁻¹(x) =
(x - 3) / 2
f(5) =
13
f⁻¹(5) =
1
Domain & Range
Domain of f:
All real numbers
Range of f:
All real numbers
Domain of f⁻¹:
All real numbers
Range of f⁻¹:
All real numbers
Verification
f(f⁻¹(x)) = x?5
f⁻¹(f(x)) = x?5
About Inverse Functions
Definition
The inverse function f⁻¹ "undoes" f. If f(a) = b, then f⁻¹(b) = a. The compositions f(f⁻¹(x)) = x and f⁻¹(f(x)) = x.
Requirements
A function must be bijective (one-to-one and onto) to have an inverse. The domain of f becomes the range of f⁻¹ and vice versa.