To find the inverse of the given function $f(x) = \frac{5}{3}x + 5$ in slope-intercept form ($y = mx + b$):

Steps:

1. Replace $f(x)$ with $y$:
   $y = \frac{5}{3}x + 5$

2. Swap $x$ and $y$ to find the inverse:
   $x = \frac{5}{3}y + 5$

3. Solve for $y$:
   $x - 5 = \frac{5}{3}y$
   Multiply through by $\frac{3}{5}$ to isolate $y$:
   $y = \frac{3}{5}(x - 5)$

4. Simplify:
   $y = \frac{3}{5}x - 3$

Final Answer:

The inverse function is:
$f^{-1}(x) = \frac{3}{5}x - 3$

Would you like a detailed explanation of any step or more examples?

5 Related Questions:

1. How do you verify that a function and its inverse are correct?
2. What does the slope of the inverse function tell us about the original function?
3. Can every function have an inverse? Why or why not?
4. How does the graph of a function relate to the graph of its inverse?
5. What happens to the y-intercept when finding the inverse?

Tip:

To verify your inverse, compose the original function and its inverse ($f(f^{-1}(x))$ and $f^{-1}(f(x))$)—both should simplify to $x$.