To find the inverse of the function \( f(x) = 3x - 1 \), follow these steps:

1. **Replace \( f(x) \) with \( y \)**:  
   \( y = 3x - 1 \)

2. **Swap \( x \) and \( y \)** (this is the step to start finding the inverse):  
   \( x = 3y - 1 \)

3. **Solve for \( y \)** (this will give the inverse function):
   \[
   x + 1 = 3y \quad \text{(add 1 to both sides)}
   \]
   \[
   y = \frac{x + 1}{3} \quad \text{(divide both sides by 3)}
   \]

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

Would you like more details or further explanation?

Here are 5 related questions for you to explore:
1. How do you verify that two functions are inverses of each other?
2. What is the inverse of \( f(x) = 4x + 5 \)?
3. How do inverse functions relate to their graphs?
4. What is the domain and range of the inverse function \( f^{-1}(x) \)?
5. Can all functions have inverses?

**Tip**: For a function to have an inverse, it must be one-to-one (i.e., it must pass the horizontal line test).

Learn how to find the inverse of the function f(x) = 3x - 1 with a detailed step-by-step solution. This problem covers key mathematical concepts, including functions, inverse functions, and the horizontal line test. Suitable for students in Grades 9-12.

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