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.

Discover how to find the inverse of the function g(x) = 3x + 4 through detailed steps. This problem covers the concept of inverse functions and includes the inverse function formula. Suitable for high school students in Grades 10-12.

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