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

1. Rewrite the function in terms of $y$: $y = (x - 3)^3$

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

3. Solve for $y$:

   • Take the cube root of both sides: $\sqrt[3]{x} = y - 3$
   • Add 3 to both sides: $y = \sqrt[3]{x} + 3$

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

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

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Would you like further details on these steps or have any other questions?

Here are 5 related questions to explore further:

1. How do you verify that a function and its inverse are correct?
2. What is the graphical relationship between a function and its inverse?
3. How does the domain and range of a function change after finding the inverse?
4. Can all functions have inverses? Why or why not?
5. How do you find the inverse of more complex functions like $y = (x^2 - 4)$?

Tip: A function's inverse, if it exists, "undoes" the action of the original function—this is like reversing an operation step-by-step.