To find the inverse of the function represented by \( y = 5(x - 2) \), follow these steps:

1. **Start with the original equation:**
   \[
   y = 5(x - 2)
   \]

2. **Swap \( y \) and \( x \):**  
   To find the inverse, replace \( y \) with \( x \) and \( x \) with \( y \).
   \[
   x = 5(y - 2)
   \]

3. **Solve for \( y \):**  
   Isolate \( y \) on one side of the equation to get the inverse function.
   \[
   \frac{x}{5} = y - 2
   \]
   \[
   y = \frac{x}{5} + 2
   \]

So, the inverse function is:
\[
y = \frac{x}{5} + 2
\]
Or more commonly written as:
\[
f^{-1}(x) = \frac{x}{5} + 2
\]

Would you like more details or have any questions? Here are 5 related questions you might find interesting:

1. How do you determine the inverse of more complex functions?
2. What is the graphical interpretation of finding an inverse function?
3. How do you verify if two functions are inverses of each other?
4. What are the conditions for a function to have an inverse?
5. How do you find the inverse of a function involving exponents?

**Tip:** Always check that your function is one-to-one (i.e., passes the horizontal line test) before finding its inverse.

Learn how to find the inverse function of y = 5(x - 2) step-by-step. This problem covers inverse functions and their formulas, suitable for students in Grades 10-12.

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