To find the inverse of the function $y = (x - 3)^3$, follow these steps:

1. Start with the given function:
   $y = (x - 3)^3$

2. Swap $x$ and $y$ to express the inverse function: $x = (y - 3)^3$

3. Solve for $y$. First, take the cube root of both sides: $\sqrt[3]{x} = y - 3$

4. Add 3 to both sides: $y = \sqrt[3]{x} + 3$

Thus, the inverse function is: $y = \sqrt[3]{x} + 3$

Looking at the options provided, the correct answer is:

D. $y = \sqrt[3]{x} + 3$

Would you like further details or clarifications?

5 Related Questions:

1. How can you verify that two functions are inverses of each other?
2. What is the graphical relationship between a function and its inverse?
3. How do you find the inverse of a more complex function, such as $y = (x + 5)^4$?
4. What are the restrictions for a function to have an inverse?
5. How does the derivative of a function relate to the derivative of its inverse?

Tip: When finding the inverse of a function, always remember to swap $x$ and $y$, then solve for $y$.