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The question asks to find \( (g \circ f)(x) \), which means \( g(f(x)) \). Given the functions:

- \( f(x) = x + 2 \)
- \( g(x) = 3x^2 + 4x + 1 \)

We need to compute \( g(f(x)) \), which involves substituting \( f(x) \) into \( g(x) \).

### Step-by-step Solution:

1. Start by substituting \( f(x) = x + 2 \) into \( g(x) \):
   \[
   g(f(x)) = g(x + 2)
   \]

2. Now, substitute \( x + 2 \) wherever there is \( x \) in \( g(x) = 3x^2 + 4x + 1 \):
   \[
   g(x + 2) = 3(x + 2)^2 + 4(x + 2) + 1
   \]

3. Expand \( (x + 2)^2 \):
   \[
   (x + 2)^2 = x^2 + 4x + 4
   \]
   So, 
   \[
   g(x + 2) = 3(x^2 + 4x + 4) + 4(x + 2) + 1
   \]

4. Expand the terms:
   \[
   g(x + 2) = 3x^2 + 12x + 12 + 4x + 8 + 1
   \]

5. Combine like terms:
   \[
   g(x + 2) = 3x^2 + (12x + 4x) + (12 + 8 + 1)
   \]
   \[
   g(x + 2) = 3x^2 + 16x + 21
   \]

Thus, \( (g \circ f)(x) = 3x^2 + 16x + 21 \).

### The correct answer is option **E**: \( 3x^2 + 16x + 21 \).

Would you like more details on any part of this process? Here are five related questions to deepen your understanding:

1. How is the composition of functions defined?
2. What is the general method to simplify \( (x + a)^2 \)?
3. How can the distributive property help in expanding expressions like \( 3(x + 2)^2 \)?
4. Can the process of function composition be reversed? How would \( f \circ g(x) \) differ here?
5. How would you approach the same problem if \( g(x) \) had a cubic term?

**Tip**: When composing functions, always make sure to substitute the entire expression for \( f(x) \) correctly into \( g(x) \).

Jika f(x) = x + 2 dan g(x) = 3x^2 + 4x + 1, maka (gof)(x) adalah....

This problem involves composing two functions: f(x) = x + 2 and g(x) = 3x^2 + 4x + 1. Learn how to compute g(f(x)) and simplify quadratic expressions step by step. Ideal for students in grades 10-12.

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