To find the inverse of the function $g(x) = 3x + 4$, follow these steps:

1. Replace $g(x)$ with $y$:

   $y = 3x + 4$

2. Swap $x$ and $y$ to find the inverse function:

   $x = 3y + 4$

3. Solve for $y$:

   $x - 4 = 3y$

   $y = \frac{x - 4}{3}$

4. Replace $y$ with $g^{-1}(x)$ to express the inverse function:

   $g^{-1}(x) = \frac{x - 4}{3}$

So, the inverse of $g(x) = 3x + 4$ is:

$g^{-1}(x) = \frac{x - 4}{3}$

Would you like more details or have any other questions? Here are some related questions:

1. How do you verify that $g^{-1}(x)$ is the correct inverse of $g(x)$?
2. What is the inverse of $f(x) = 2x + 5$?
3. How do you find the inverse of a quadratic function?
4. What is the graph of $g^{-1}(x) = \frac{x - 4}{3}$?
5. How does the domain of $g(x)$ relate to the range of $g^{-1}(x)$?

Tip: When finding the inverse of a function, make sure to swap the variables and solve for the new dependent variable to find the correct inverse function.