Inverse Functions Calculator
Find inverse functions and verify with composition
Supported: linear, quadratic, sqrt, exp, ln, 1/x
Risultati
Inserisci i valori e clicca Calcola per vedere il risultato.
Theory & Formula
Inverse Functions
An inverse function reverses the action of the original function.
Definition
\(f(f^{-1}(x)) = x \text{ and } f^{-1}(f(x)) = x\)
f and f⁻¹ undo each other
Finding an Inverse
- Write y = f(x)
- Swap x and y
- Solve for y to get f⁻¹(x)
Properties
One-to-One Required: Only one-to-one functions have inverses
Reflection: Graph of f⁻¹ is reflection of f across y=x
Domain/Range: Domain of f = Range of f⁻¹
Example
Find the inverse of f(x) = 2x + 3:
\(f(x) = 2x + 3\)\(y = 2x + 3\)\(x = 2y + 3\)\(2y = x - 3\)\(y = \frac{x - 3}{2}\)\(f^{-1}(x) = \frac{x - 3}{2}\)