Welcome to our exploration of inverse functions. An inverse function reverses the mapping of the original function. If the original function maps x to y, then the inverse function maps y back to x. The key insight is that these functions undo each other's operations.
A fundamental property of inverse functions is that their domains and ranges are swapped. The domain of the original function becomes the range of the inverse function, and the range of the original function becomes the domain of the inverse function. This reciprocal relationship is essential for understanding how inverse functions work.