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To find \((f \circ f)(x)\), we need to calculate the composition of the function \(f(x)\) with itself.

Given:
- \(f(x) = x + 2\)

Now, \((f \circ f)(x)\) means \(f(f(x))\). We substitute \(f(x)\) into itself:

\[
f(f(x)) = f(x + 2)
\]

To find \(f(x + 2)\), substitute \(x + 2\) into the function \(f(x)\):

\[
f(x + 2) = (x + 2) + 2 = x + 4
\]

Thus, \((f \circ f)(x) = x + 4\).

Let me know if you would like any further clarifications! Here are some related questions for further practice:

1. What is \((f \circ h)(x)\) if \(h(x) = x^2 - 3\)?
2. How would you calculate \((h \circ f)(x)\)?
3. What is the result of \((f \circ f \circ f)(x)\)?
4. How does the behavior of the function \(f(x) = x + 2\) change as you repeatedly compose it with itself?
5. If \(f(x) = 2x\), what would \((f \circ f)(x)\) be?

**Tip:** Composition of functions can be thought of as substituting one function's output into another's input.

What is (f ∘ f)(x) given f(x) = x + 2 and h(x) = x^2 - 3?

Learn how to solve the function composition problem (f ∘ f)(x) with a step-by-step guide, using the function f(x) = x + 2. This example demonstrates basic function composition and is suitable for students in Grades 9-11.

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