A manufacturing company uses the function $f(x) = 4x + 7$ to calculate the total cost of production, where $x$ represents the number of units produced. To determine a formula for the number of units based on a known cost, the production manager needs to find the inverse function. Arrange the following steps in the correct order to find the inverse of $f(x) = 4x + 7$.

A billing specialist is reviewing a new automated pricing model and determines that the inverse of the pricing function $f(x) = 4x + 7$ is $f^{-1}(x) = \frac{x - 7}{4}$. According to the standard algebraic procedure, which specific step must they recall and perform to verify that this inverse function is completely accurate?

A billing specialist at a local utility company uses the function $f(x) = 4x + 7$ to determine a customer's total bill, where $x$ represents the hours of service. To create a lookup tool that finds the number of hours $(x)$ from a known total bill $(y)$, the specialist needs to document the algebraic steps to find the inverse function. Match each procedural step of the inversion process with the specific equation it produces for this function.

Inverse Function for Expense Modeling

A logistics coordinator for a local delivery service uses the linear function $f(x) = 4x + 7$ to calculate the total shipping cost based on the package weight in pounds, $x$. To create a tool that calculates weight from cost, the coordinator follows the standard algebraic procedure to find the inverse function. True or False: According to this procedure, the step of interchanging the variables $x$ and $y$ for this function results in the equation $x = 4y + 7$.

Recalling Steps to Invert a Package Cost Function

A customer support coordinator at a SaaS company uses the linear billing model $f(x) = 4x + 7$ to calculate a client's monthly fee, where $x$ represents the number of active user licenses. To build an automated calculator that retrieves the number of active licenses from a known total bill, the coordinator needs to find the inverse function, $f^{-1}(x)$. Following the standard algebraic procedure, they substitute $y$ for $f(x)$ to obtain the equation $y = 4x + 7$, and then interchange the variables $x$ and $y$. What expression does $x$ equal immediately after interchanging the variables? Complete the equation below:

$x =$ ____