Inverse of Composite Functions

Inverse of Composite Functions

## Formula

$$(g\circ f)^{-1}=f^{-1}\circ g^{-1}$$

## Conditions / Special Cases

Both $$f$$ and $$g$$ must be invertible.

For three invertible functions:

$$(f\circ g\circ h)^{-1}=h^{-1}\circ g^{-1}\circ f^{-1}$$

## Usage

- Used to find the inverse of composite functions without directly solving the complete expression.