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From the image you provided, the question appears to involve composite functions, where \( f(x) \) and \( g(x) \) are given as:

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

The task is to find various composite functions and values, such as:

- \( (f \circ g)(0) \)
- \( (g \circ f)(3) \)
- \( (g \circ f)(x) = 8 \), solve for \( x \)

### Step-by-Step Solution:

#### 1. \( (f \circ g)(0) \)
This is the value of \( f(g(0)) \).
- First, find \( g(0) \):
  \[
  g(0) = 0^2 - 3(0) + 4 = 4
  \]
- Now, substitute \( g(0) = 4 \) into \( f(x) \):
  \[
  f(4) = 2(4) + 1 = 8 + 1 = 9
  \]
Thus, \( (f \circ g)(0) = 9 \).

#### 2. \( (g \circ f)(3) \)
This is the value of \( g(f(3)) \).
- First, find \( f(3) \):
  \[
  f(3) = 2(3) + 1 = 6 + 1 = 7
  \]
- Now, substitute \( f(3) = 7 \) into \( g(x) \):
  \[
  g(7) = 7^2 - 3(7) + 4 = 49 - 21 + 4 = 32
  \]
Thus, \( (g \circ f)(3) = 32 \).

#### 3. Solve \( (g \circ f)(x) = 8 \)
This means we need to solve for \( x \) such that \( g(f(x)) = 8 \).
- First, find \( f(x) \):
  \[
  f(x) = 2x + 1
  \]
- Now, substitute \( f(x) \) into \( g(x) \):
  \[
  g(f(x)) = (2x + 1)^2 - 3(2x + 1) + 4
  \]
- Simplify the expression:
  \[
  (2x + 1)^2 = 4x^2 + 4x + 1
  \]
  \[
  -3(2x + 1) = -6x - 3
  \]
  \[
  g(f(x)) = 4x^2 + 4x + 1 - 6x - 3 + 4 = 4x^2 - 2x + 2
  \]
- Now, solve \( 4x^2 - 2x + 2 = 8 \):
  \[
  4x^2 - 2x + 2 - 8 = 0
  \]
  \[
  4x^2 - 2x - 6 = 0
  \]
  Divide through by 2:
  \[
  2x^2 - x - 3 = 0
  \]
- Solve using the quadratic formula:
  \[
  x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4(2)(-3)}}{2(2)}
  \]
  \[
  x = \frac{1 \pm \sqrt{1 + 24}}{4} = \frac{1 \pm \sqrt{25}}{4}
  \]
  \[
  x = \frac{1 \pm 5}{4}
  \]
Thus, \( x = \frac{1 + 5}{4} = \frac{6}{4} = 1.5 \) or \( x = \frac{1 - 5}{4} = \frac{-4}{4} = -1 \).

So, the solutions are \( x = 1.5 \) and \( x = -1 \).

---

Would you like more details or have any questions?

Here are 5 related questions for further practice:

1. What is \( (f \circ g)(x) \) in general form?
2. How would you solve \( (f \circ g)(x) = 5 \)?
3. Can you find \( (g \circ f)(0) \)?
4. What are the solutions to \( g(f(x)) = 16 \)?
5. If \( f(x) = 3x - 2 \) and \( g(x) = x^2 + x + 1 \), what is \( (f \circ g)(2) \)?

**Tip:** Always check the order of composition carefully—\( f(g(x)) \) is not the same as \( g(f(x)) \)!

Tentukan nilai dari (f o g)(0), (g o f)(3), dan solusi dari (g o f)(x) = 8, maka x?

Learn how to solve composite function problems involving (f o g)(0), (g o f)(3), and find x for (g o f)(x) = 8 with detailed step-by-step explanations. Suitable for students in Grades 10-12 studying Algebra and Quadratic Equations.

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