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

1. Start with the equation $y = (x - 3)^3$.
2. Swap $x$ and $y$ to find the inverse: $x = (y - 3)^3$
3. Now, solve for $y$. Take the cube root of both sides: $\sqrt[3]{x} = y - 3$
4. Add 3 to both sides: $y = \sqrt[3]{x} + 3$

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

Thus, the correct answer is: D. $y = \sqrt[3]{x} + 3$

Would you like more details or have any questions?

Here are 5 related questions for further practice:

1. What is the inverse of $y = (x + 2)^3$?
2. How do you verify if two functions are inverses of each other?
3. What is the general method to find the inverse of a cubic function?
4. If $f(x) = (x - 5)^3$, what is the inverse of $f(x)$?
5. What happens to the graph of a function when you find its inverse?

Tip: The inverse of a function reflects the original function over the line $y = x$.