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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.

For the function f(x) = 2(x + 10), find f^{-1}(x).

Explore how to find the inverse function of f(x) = 2(x + 10) with a step-by-step solution. This problem involves key algebraic concepts and the inverse function formula, suitable for students in Grades 9-12.

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