To find the inverse function $f^{-1}(x)$ for the given function $f(x) = 2(x + 10)$, follow these steps:

1. Rewrite the function: Start by expressing $y$ in terms of $x$. $y = 2(x + 10)$

2. Swap $x$ and $y$: To find the inverse, switch the roles of $x$ and $y$. $x = 2(y + 10)$

3. Solve for $y$: Isolate $y$ to express it as a function of $x$. $\frac{x}{2} = y + 10$ $y = \frac{x}{2} - 10$

So, the inverse function is: $f^{-1}(x) = \frac{x}{2} - 10$

From the options provided in the image, the correct choice is: $\circ \quad f^{-1}(x) = \frac{x}{2} - 10$

Would you like any further details on this solution, or do you have any additional questions?

Here are 5 related questions to consider:

1. How do you find the inverse of more complex functions?
2. What is the domain and range of the inverse function $f^{-1}(x)$?
3. How do the graphs of $f(x)$ and $f^{-1}(x)$ relate to each other?
4. Can all functions have an inverse? Why or why not?
5. What are some practical applications of inverse functions?

Tip: When finding the inverse function, always ensure the function is one-to-one, meaning it passes the horizontal line test. This guarantees that the inverse will also be a function.