The problem asks us to find the inverse of the function $y = 4x - 7$. We are given five options and need to determine which one represents the inverse function.

1. Problem Description

The problem asks us to find the inverse of the function $y = 4x - 7$. We are given five options and need to determine which one represents the inverse function.

2. Solution Steps

To find the inverse of a function, we switch $x$ and $y$ and then solve for $y$.

Given the function $y = 4x - 7$.

First, switch $x$ and $y$:

$x = 4y - 7$

Now, solve for $y$:

$x + 7 = 4y$

$y = \frac{x + 7}{4}$

$y = \frac{x + 7}{4}$ can also be written as $x = \frac{y + 7}{4}$.

Option D is $x = (y + 7) \div 4$, which is the same as $x = \frac{y + 7}{4}$.

3. Final Answer

D. $x = (y + 7) \div 4$