To solve the composition of the function \((f \circ f)(x) = x^2 + 3x + 2\), we need to first express what \(f(x)\) is and then substitute it back into itself.

### Step 1: Assume \( f(x) = x^2 + 3x + 2 \)
Given the expression, we assume:
\[
f(x) = x^2 + 3x + 2
\]

### Step 2: Substitute \(f(x)\) into itself to find \((f \circ f)(x)\)
\[
(f \circ f)(x) = f(f(x))
\]
Now substitute \(f(x)\) into itself:
\[
f(f(x)) = f(x^2 + 3x + 2)
\]

### Step 3: Replace \(x\) in \(f(x)\) with \(x^2 + 3x + 2\)
Substitute \(x^2 + 3x + 2\) into the function:
\[
f(x^2 + 3x + 2) = (x^2 + 3x + 2)^2 + 3(x^2 + 3x + 2) + 2
\]

### Step 4: Expand and simplify
First, expand \((x^2 + 3x

Explore how to solve the function composition problem (f ° f)(x) = x² + 3x + 2 step-by-step. Learn about function composition and quadratic equations, suitable for high school students.

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