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To find the inverse function \( f^{-1}(x) \) for the given function \( f(x) = 3x - 8 \), follow these steps:

### Steps:
1. Start by replacing \( f(x) \) with \( y \):
   \[
   y = 3x - 8
   \]
   
2. Swap \( x \) and \( y \) to start solving for the inverse:
   \[
   x = 3y - 8
   \]

3. Solve for \( y \):
   \[
   x + 8 = 3y
   \]
   \[
   y = \frac{x + 8}{3}
   \]

4. Finally, replace \( y \) with \( f^{-1}(x) \):
   \[
   f^{-1}(x) = \frac{x + 8}{3}
   \]

So, the inverse function is:
\[
f^{-1}(x) = \frac{x + 8}{3}
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you verify if a function is one-to-one (invertible)?
2. How do you check if two functions are inverses of each other?
3. What is the inverse of a quadratic function?
4. How does the inverse of a linear function compare to the original?
5. What transformations occur when taking the inverse of a function?

**Tip:** Always swap \( x \) and \( y \) when finding the inverse of a function to solve for the new variable.

Find the inverse function f^(-1)(x) for the given function f(x). f(x) = 3x - 8

Learn how to find the inverse of the function f(x) = 3x - 8 with a step-by-step solution. This problem involves core algebraic concepts, including inverse functions and the inverse function theorem. Suitable for high school students (Grades 9-12).

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