To find the inverse of the function $y = 3\sqrt{1 - x^3}$, we need to express $x$ in terms of $y$. Let's go through the steps to find the inverse function.

1. Start with the given equation: $y = 3\sqrt{1 - x^3}$

2. Isolate the square root term: $\frac{y}{3} = \sqrt{1 - x^3}$

3. Square both sides to eliminate the square root: $\left(\frac{y}{3}\right)^2 = 1 - x^3$

4. Simplify: $\frac{y^2}{9} = 1 - x^3$

5. Isolate $x^3$: $x^3 = 1 - \frac{y^2}{9}$

6. Solve for $x$: $x = \sqrt[3]{1 - \frac{y^2}{9}}$

Thus, the inverse function is: $f^{-1}(y) = \sqrt[3]{1 - \frac{y^2}{9}}$

If you have any questions or want further details, feel free to ask!

Here are 5 more questions you can ask:

1. How do you find the derivative of $f(x) = x^3 + 2x + 1$?
2. What is the integral of $\sin(x)$?
3. Can you solve the quadratic equation $x^2 - 4x + 4 = 0$?
4. How do you simplify the expression $\frac{2x^2 - 8x + 8}{2}$?
5. What is the limit of $\frac{1}{x}$ as $x$ approaches infinity?

Tip: Always check your work by substituting back into the original equation to ensure the inverse is correct.