To express a function as the composition of two functions $f(g(x))$, we are typically asked to break down a given function into two separate functions, $f$ and $g$, such that when composed, they reproduce the original function.

The notation $(f \circ g)(2)$, or $f(g(2))$, means that we first evaluate $g(2)$, and then apply the function $f$ to the result.

To proceed:

1. If you have a specific function in mind that needs to be expressed as $f(g(x))$, please share it. Otherwise, I will explain the general idea with an example.

Let's consider the following function for illustration:

$h(x) = (3x + 1)^2$

We can express $h(x)$ as the composition $f(g(x))$ by defining:

• $g(x) = 3x + 1$
• $f(x) = x^2$

So, the composition would be:

$f(g(x)) = (g(x))^2 = (3x + 1)^2$

Now, to evaluate $(f \circ g)(2)$, we first find $g(2)$:

$g(2) = 3(2) + 1 = 7$

Then, apply $f$ to this result:

$f(7) = 7^2 = 49$

Thus, $(f \circ g)(2) = 49$.

If you had a specific function in mind, let me know, and I can adjust the explanation to match it!

Would you like more details or have any questions? Here are five related questions:

1. Can you provide a specific function you want to decompose into $f(g(x))$?
2. How would you decompose a more complex function, such as $h(x) = \sin(x^2 + 1)$?
3. What happens when you reverse the order of the composition, i.e., $g(f(x))$?
4. Can all functions be written as the composition of two functions?
5. How does function composition relate to inverse functions?

Tip: When decomposing a function, try to identify the "inner" and "outer" operations, which can help in defining $g(x)$ and $f(x)$ clearly.