To express the function $(f - g)(x)$ as a composition of functions in the form $f(g(x))$, let's first clarify the expression $(f - g)(x)$ and then find the composition.

Given:

$(f - g)(x) = f(x) - g(x)$

To find $(f - g)(2)$, you would first evaluate $f(2)$ and $g(2)$, and subtract them:

$(f - g)(2) = f(2) - g(2)$

However, the question asks to express this as a composition $f(g(x))$. Here’s how you can proceed:

Step-by-step breakdown:

1. Original form: $(f - g)(x) = f(x) - g(x)$
2. Composition form: The idea of $f(g(x))$ implies that you are applying the function $g(x)$ first, and then plugging that result into the function $f$.

Since the problem asks for composition and $(f - g)(2)$, we need to make assumptions or use specific forms for $f$ and $g$ to show the composition.

Let’s assume:

• $g(x) = x$ (this would make the composition easier to express).
• Then $f(g(x)) = f(x)$, which leads us back to the original form.

If you were trying to express a combination such as $f(g(x)) = h(x)$, then it would depend on the specific definitions of $f(x)$ and $g(x)$.

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Would you like to provide specific forms of $f(x)$ and $g(x)$, or should I walk you through a detailed example?

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Relative Questions:

1. How would you define $f(x)$ and $g(x)$ in this case?
2. Do you want examples with specific functions for $f(x)$ and $g(x)$?
3. Would you like to explore how compositions work for different function types (e.g., polynomials)?
4. How would this change if the expression was $(f + g)(x)$?
5. Do you need help with evaluating $f(g(x))$ for a particular input?

Tip:

When dealing with compositions of functions, always start by applying the innermost function first, then use the result as the input for the outer function.