To find \((f - g)(x)\), we need to subtract the function \(g(x)\) from \(f(x)\).

Given:
- \(f(x) = x - 8\)
- \(g(x) = \sqrt{x} + 2\)

Now, subtract \(g(x)\) from \(f(x)\):

\[
(f - g)(x) = f(x) - g(x)
\]
\[
(f - g)(x) = (x - 8) - (\sqrt{x} + 2)
\]
Simplify:

\[
(f - g)(x) = x - 8 - \sqrt{x} - 2
\]
\[
(f - g)(x) = x - \sqrt{x} - 10
\]

Thus, \((f - g)(x) = x - \sqrt{x} - 10\).

Would you like further clarification or additional examples?

Here are five related questions:
1. What is \((f + g)(x)\)?
2. Can you find \((f \cdot g)(x)\)?
3. What is \((f \div g)(x)\), assuming \(g(x) \neq 0\)?
4. What is the domain of \((f - g)(x)\)?
5. How does the behavior of \((f - g)(x)\) change as \(x \to \infty\)?

**Tip:** Always remember to check the domain restrictions for square roots or divisions when working with composite functions!

f(x) = x - 8, g(x) = √x + 2. Find (f - g)(x).

Learn how to find the difference between two functions, f(x) = x - 8 and g(x) = √x + 2. This problem covers key algebraic concepts, including function operations and square root expressions, and is suitable for students in Grades 9-11.

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