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We are tasked with finding the inverse of the function \( y = 3x - 8 \) and determining which of the options (A, B, C, or D) is equivalent to this inverse.

### Steps to find the inverse:
1. Start with the equation: 
   \[
   y = 3x - 8
   \]
2. Swap \( x \) and \( y \) (this is the process for finding the inverse function):
   \[
   x = 3y - 8
   \]
3. Solve for \( y \):
   \[
   x + 8 = 3y
   \]
   \[
   y = \frac{x + 8}{3}
   \]
   This is the inverse function.

### Now, let's examine the choices:
- **A:** \( y = \frac{1}{3x - 8} \) — This is not equivalent to the inverse function.
- **B:** \( y = \frac{3}{x} - 8 \) — Also not equivalent.
- **C:** \( -y = -3x + 8 \) — Simplifying this: \( y = 3x - 8 \), which is just the original function, not the inverse.
- **D:** \( x = 3y - 8 \) — This matches the equation we had right before solving for \( y \), so this is equivalent to the inverse.

### Correct Answer: **D**

Would you like further clarification or more details on this problem?

Here are some related questions:
1. How do you verify an inverse function?
2. What is the significance of swapping \( x \) and \( y \) when finding an inverse?
3. Can a function always have an inverse?
4. How do horizontal line tests relate to inverse functions?
5. How do you graph the inverse of a function?

**Tip:** To check if two functions are inverses, you can compose them: if \( f(f^{-1}(x)) = x \) and \( f^{-1}(f(x)) = x \), then they are inverses.

Brody wants to write the inverse function of y = 3x - 8. Which of the following is mathematically equivalent to the inverse function?

Learn how to find the inverse function of y = 3x - 8. Follow the step-by-step process to solve for the inverse, identify the correct option, and understand the core concepts of inverse functions and linear equations. Suitable for students in Grades 9-12.

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