To find the inverse of the function \( J(x) = 4x - 1 \), we follow these steps:

1. **Replace \( J(x) \) with \( y \):**
   \[
   y = 4x - 1
   \]

2. **Swap \( x \) and \( y \) to find the inverse:**
   \[
   x = 4y - 1
   \]

3. **Solve for \( y \) in terms of \( x \):**

   \[
   x + 1 = 4y
   \]
   \[
   y = \frac{x + 1}{4}
   \]

4. **Replace \( y \) with \( J^{-1}(x) \):**
   \[
   J^{-1}(x) = \frac{x + 1}{4}
   \]

So, the inverse of the function \( J(x) = 4x - 1 \) is:
\[
J^{-1}(x) = \frac{x + 1}{4}
\]

Would you like more details, or do you have any questions?

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Here are five related questions you might find interesting:

1. How do you verify if two functions are inverses of each other?
2. What is the inverse of \( J(x) = 4x + 3 \)?
3. How do you find the inverse of a quadratic function?
4. What happens to the graph of a function when you find its inverse?
5. How do you interpret the inverse of a function in real-world contexts?

**Tip:** When finding the inverse of a function, always check if the function is one-to-one, meaning that each \( y \)-value corresponds to exactly one \( x \)-value. This ensures that the inverse is also a function.

Learn how to find the inverse of the function J(x) = 4x - 1 with a detailed step-by-step solution. This problem covers the concept of inverse functions in algebra. Suitable for students in Grades 11-12.

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