The image contains a problem related to inverse functions. Let's break down the information provided:

The given functions are:

• $f(x) = 2(x + 10)$
• $g(x) = 2(x - 10)$

The task asks to find $f(g(x))$ and $g(f(x))$.

To solve this:

1. Find $f(g(x))$: Substitute $g(x) = 2(x - 10)$ into $f(x)$.

   $f(g(x)) = f(2(x - 10)) = 2(2(x - 10) + 10)$ Simplify the expression inside the parentheses: $f(g(x)) = 2(2x - 20 + 10) = 2(2x - 10) = 4x - 20$

2. Find $g(f(x))$: Substitute $f(x) = 2(x + 10)$ into $g(x)$.

   $g(f(x)) = g(2(x + 10)) = 2(2(x + 10) - 10)$ Simplify the expression inside the parentheses: $g(f(x)) = 2(2x + 20 - 10) = 2(2x + 10) = 4x + 20$

Thus:

• $f(g(x)) = 4x - 20$
• $g(f(x)) = 4x + 20$

Let me know if you'd like further clarification or if you have any more questions!

Related questions:

1. What are the properties of inverse functions?
2. How do you determine if two functions are inverses of each other?
3. How do you check the correctness of inverse functions?
4. What happens if you compose a function with its inverse?
5. How can you find inverse functions algebraically?

Tip: When working with inverse functions, one way to check if two functions are inverses of each other is to see if $f(g(x)) = x$ and $g(f(x)) = x$.