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.