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To find the inverse of the function \( y - 2 = 3x \), we follow these steps:

1. **Rewrite the function** in terms of \( y \):
   \[
   y - 2 = 3x
   \]
   Add 2 to both sides:
   \[
   y = 3x + 2
   \]

2. **Swap** \( x \) and \( y \) to find the inverse:
   \[
   x = 3y + 2
   \]

3. **Solve for \( y \)** (the inverse function):
   \[
   x - 2 = 3y
   \]
   Divide both sides by 3:
   \[
   y = \frac{x - 2}{3}
   \]

Thus, the inverse of the function is \( y = \frac{x - 2}{3} \), which matches **option C**.

### Answer: **C** \( y = \frac{x - 2}{3} \)

Would you like more details or have any questions?

Here are some related questions for further understanding:
1. What is the general method for finding the inverse of a linear function?
2. How do you verify if a function and its inverse are correct?
3. Can every function have an inverse? Why or why not?
4. What are the key differences between solving for the inverse of a linear vs non-linear function?
5. How does the graph of a function relate to its inverse?

**Tip:** When finding the inverse of a function, swapping \( x \) and \( y \) is essential before solving for \( y \) again.

What is the inverse of the function y - 2 = 3x?

Learn how to find the inverse of the linear function y - 2 = 3x with detailed steps. This problem covers key algebraic concepts and is suitable for students in Grades 9-11.

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