Domain and Range of an Inverse Function

Example: Finding the Inverse of the Function $\{(0,3),(1,5),(2,7),(3,9)\}$

Inverse Function Notation

Example: Finding the Inverse of the Function $\{(0, 4), (1, 7), (2, 10), (3, 13)\}$

Finding an Inverse Function Using an Algebraic Equation

A company directory uses a function $f$ to map employee badge numbers to their assigned office room numbers: $f = \{(1050, 12), (2100, 14), (3150, 16)\}$. To create a reverse lookup that finds a badge number based on a room number, the system uses the inverse function $f^{-1}$. Which of the following represents the set of ordered pairs for $f^{-1}$?

An HR database uses a one-to-one function to map an employee's starting year ($x$) to their earned vacation days ($y$), written as the ordered pair $(x, y)$. To define the inverse function that maps vacation days back to the starting year, you must form new ordered pairs by ________ the $x$- and $y$-coordinates of each original pair.

Retail Inventory Reverse Lookup

In a company's asset management database, a one-to-one function is used to link unique hardware tags to specific office workstations. Match each original assignment pair (Hardware Tag, Workstation ID) with its corresponding inverse pair (Workstation ID, Hardware Tag) used for reverse-lookup audits.

A corporate security system uses a function to map unique employee identification numbers ($x$) to their designated office security codes ($y$) using the set of ordered pairs $(x, y)$. To define the inverse function $f^{-1}$, which identifies an employee identification number when given a security code, you must reverse each ordered pair to $(y, x)$.

Example: Verifying that $f(x) = 5x - 1$ and $g(x) = \frac{x+1}{5}$ are Inverse Functions

Finding an Inverse Function Using an Algebraic Equation

A software developer is testing two conversion tools used in a logistics application. The first tool uses a function $f(x)$ to convert pallet weights into kilograms, and the second tool uses a function $g(x)$ to convert kilograms back into pallet weights. To verify that these two tools are mathematically inverse functions, which condition must be met for any input $x$?

A logistics coordinator is testing two conversion formulas: $f(x)$ to convert warehouse pallets to individual boxes, and $g(x)$ to convert boxes back to pallets. To mathematically verify that these two formulas are inverse functions, it is sufficient to prove only that $f(g(x)) = x$, and checking $g(f(x)) = x$ is unnecessary.

Verifying Currency Conversion Inverses

A software quality assurance (QA) team is testing a pair of conversion algorithms for a global shipping company: one that converts package weight from pounds to kilograms and another that converts it back. To verify these are true inverse functions, the team must recognize specific mathematical components of the verification process. Match each term or expression with its correct role in this process.

Verifying Inventory System Inverses