Inverse Functions

An inverse function reverses what a one-to-one function does. If a function f maps each value in its domain to a value in its range, its inverse, f inverse, maps each value in the range back to the corresponding value in the domain. This means the domain and range switch.

Imagine an architect drawing a floor plan using a fixed scale. Suppose 1 centimeter on the plan represents 200 centimeters in the actual building.

This scale can be represented as a function that maps actual measurements to plan measurements. Here, actual measurements form the domain, and plan measurements form the range.

Now, suppose a builder measures a wall on the plan as 3 centimeters and wants to find its actual measurement. To find it, the builder uses the inverse function, which multiplies plan measurements by 200.

For example, the original function maps 600 centimeters in the building to 3 centimeters on the plan. The inverse function reverses this mapping, so 3 centimeters on the plan maps back to 600 centimeters in the building.

In the inverse function, plan measurements form the domain, while actual measurements form the range.