An inventory management system uses a function $P(n)$ to calculate the total price of $n$ items. When the system needs to determine the number of items based on a total price, the documentation refers to the inverse function $P^{-1}(x)$. In this notation, what is the primary purpose of the superscript $-1$?

A financial model uses the function $R(x)$ to project weekly revenue based on $x$ units sold. If a business analyst sees the notation $R^{-1}(x)$ in the model's documentation, this indicates the reciprocal of the revenue function, meaning they should calculate $\frac{1}{R(x)}$.

A warehouse logistics manager uses a function $W(n)$ to calculate the total weight of a shipment based on the number of units $n$. To find the number of units when the weight is known, the manager uses the inverse function. Match each part of the inverse notation with its correct description or meaning.

Inverse Function Notation in Revenue Modeling

A logistics coordinator uses a function $T(d)$ to determine the time required for a truck to travel a distance $d$. To calculate the distance that can be covered given a specific amount of time, the coordinator uses the notation $T^{-1}(y)$. In this mathematical notation, the superscript $-1$ is a specialized symbol indicating that $T^{-1}$ is the ____ function.