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

1. **Replace** \( m(x) \) with \( y \):
   \[
   y = -4x + 1
   \]
   
2. **Swap** \( x \) and \( y \) to solve for the inverse:
   \[
   x = -4y + 1
   \]

3. **Solve for** \( y \):
   \[
   x - 1 = -4y
   \]
   \[
   y = \frac{x - 1}{-4}
   \]
   \[
   y = -\frac{x - 1}{4}
   \]

4. Therefore, the inverse function is:
   \[
   m^{-1}(x) = -\frac{x - 1}{4}
   \]

Would you like further explanation or have any questions on this?

Here are five related questions:
1. What are the steps to verify if two functions are inverses?
2. How can we find the domain and range of the inverse function?
3. What is the graphical relationship between a function and its inverse?
4. How does the slope of a linear function affect its inverse?
5. Can a quadratic function have an inverse?

**Tip**: To quickly check if two functions are inverses, compose them (i.e., \( f(f^{-1}(x)) \) and \( f^{-1}(f(x)) \)) and see if the result is \( x \).

Learn how to find the inverse of the linear function m(x) = -4x + 1 with a step-by-step solution. This problem covers key algebraic concepts, including solving for inverse functions. Suitable for students in Grades 9-11.

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