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.

Learn how to find the inverse function of y = 3sqrt(1 - x^3) step-by-step. This problem involves inverse functions, cube roots, and square roots. Suitable for students in Grades 11-12.

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