Find the inverse function in slope-intercept form (mx+b):
f, of, x, equals, start fraction, 5, divided by, 2, end fraction, x, minus, 5


The given function is:

\[
f(x) = \frac{5}{2}x - 5
\]

### Steps to find the inverse of this function:

1. **Replace \( f(x) \) with \( y \):**
   \[
   y = \frac{5}{2}x - 5
   \]

2. **Swap \( x \) and \( y \) to begin finding the inverse:**
   \[
   x = \frac{5}{2}y - 5
   \]

3. **Solve for \( y \) (the inverse function):**
   - Add 5 to both sides:
     \[
     x + 5 = \frac{5}{2}y
     \]
   - Multiply both sides by \( \frac{2}{5} \) to isolate \( y \):
     \[
     y = \frac{2}{5}(x + 5)
     \]

4. **Rewrite the result:**
   \[
   f^{-1}(x) = \frac{2}{5}(x + 5)
   \]

This is the inverse function in slope-intercept form.

Would you like more details on any of these steps? Here are some follow-up questions that can expand your understanding:

1. How do you verify if two functions are inverses of each other?
2. What is the slope of the inverse function, and how does it relate to the original?
3. Can every function be inverted? Why or why not?
4. How does transforming the function affect its graph?
5. What are real-life applications of finding inverse functions?

**Tip:** The graph of a function and its inverse are symmetric with respect to the line \( y = x \).

Find the inverse function in slope-intercept form (mx+b): f(x) = (5/2)x - 5

Discover how to find the inverse of the function f(x) = (5/2)x - 5 in slope-intercept form. This guide walks you through the steps of solving for the inverse function, covering key algebraic concepts and the use of the slope-intercept formula. Ideal for students in Grades 9-12.

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