Which of the following is the inverse of y=(x−3)3y=(x−3)3?

A.y=x−3−−−−−√3y=x−33

B.y=x+3−−−−−√3y=x+33

C.y=x−−√3−3y=x3−3

D.y=x−−√3+3y=x3+3

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 \( y = x \).

Which of the following is the inverse of y = (x - 3)^3?

Learn how to find the inverse of the cubic function y = (x - 3)^3 with a step-by-step guide. This problem covers key algebraic concepts, including inverse functions and cubic transformations. Ideal for high school students in Grades 10-12.

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