The image shows a mathematical problem in Indonesian that translates to:

"If $f(x) = 2x - 6$, then $f^{-1}(x) =$ ..."

To find the inverse of the function $f(x) = 2x - 6$, follow these steps:

1. Replace $f(x)$ with $y$:
   $y = 2x - 6$

2. Swap $x$ and $y$ to find the inverse function:
   $x = 2y - 6$

3. Solve for $y$:
   $x + 6 = 2y$
   $y = \frac{x + 6}{2}$

4. Replace $y$ with $f^{-1}(x)$:
   $f^{-1}(x) = \frac{x + 6}{2}$

So, the inverse function is $f^{-1}(x) = \frac{x + 6}{2}$.

Would you like more details or have any questions?

Here are 5 related questions to explore further:

1. How do you find the inverse of a linear function in general?
2. What are the graphical interpretations of a function and its inverse?
3. What is the domain and range of $f(x) = 2x - 6$ and $f^{-1}(x)$?
4. What happens if you compose a function with its inverse, $f(f^{-1}(x))$?
5. How does finding the inverse change if the function is not linear?

Tip: When finding the inverse of a function, always ensure that the original function is one-to-one, meaning it passes the horizontal line test.