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The given function is \( f(x) = \frac{|2x - 4|}{2 - x} \), and the question asks which statements about this function are correct.

### Let's analyze each statement one by one:

1. **\( f(2) \)**: 
   \[
   f(2) = \frac{|2(2) - 4|}{2 - 2} = \frac{|4 - 4|}{0} = \frac{0}{0} \quad \text{(undefined)}
   \]
   So, the **value of \( f(2) \) does not exist**.

2. **Limits as \( x \to 2 \)**:
   
   The behavior of the function around \( x = 2 \) needs to be checked by approaching from the left and right:
   
   - For \( x \to 2^+ \) (approaching 2 from the right):
     - When \( x > 2 \), \( |2x - 4| = 2x - 4 \), so the function becomes:
       \[
       f(x) = \frac{2x - 4}{2 - x}
       \]
       As \( x \to 2^+ \), the denominator \( 2 - x \) approaches 0 from the negative side, and the numerator \( 2x - 4 \) approaches 0 from the positive side. Therefore:
       \[
       \lim_{x \to 2^+} f(x) = -\infty
       \]

   - For \( x \to 2^- \) (approaching 2 from the left):
     - When \( x < 2 \), \( |2x - 4| = -(2x - 4) = 4 - 2x \), so the function becomes:
       \[
       f(x) = \frac{4 - 2x}{2 - x}
       \]
       As \( x \to 2^- \), the denominator \( 2 - x \) approaches 0 from the positive side, and the numerator \( 4 - 2x \) approaches 0 from the positive side. Therefore:
       \[
       \lim_{x \to 2^-} f(x) = +\infty
       \]

   Since the one-sided limits do not match, the two-sided limit does **not exist**.

3. **Other limits and values**:
   
   - \( \lim_{x \to 0^+} f(x) \): 
     \[
     f(x) = \frac{|2x - 4|}{2 - x}
     \]
     As \( x \to 0^+ \), the numerator approaches 4 and the denominator approaches 2, so:
     \[
     \lim_{x \to 0^+} f(x) = \frac{4}{2} = 2
     \]

---

### Correct Answers:
- (a) \( f(2) \) does not exist.
- (d) \( \lim_{x \to 2} f(x) \) does not exist.
- (g) \( \lim_{x \to 2} f(x) \) exists (this statement is **false**).
- (h) \( \lim_{x \to 0^+} f(x) = 2 \).

### Would you like more details or explanations about any part of the solution?

Here are 5 follow-up questions to deepen understanding:
1. Why does \( f(2) \) result in an undefined form \( \frac{0}{0} \)?
2. How does the behavior of \( f(x) \) change when \( x \to 2 \) from the left and right?
3. What is the significance of checking one-sided limits in this problem?
4. Why does \( \lim_{x \to 2^+} f(x) = -\infty \) but \( \lim_{x \to 2^-} f(x) = +\infty \)?
5. How can we verify limits analytically using the piecewise nature of absolute values?

**Tip**: Always evaluate one-sided limits separately when there is an absolute value function involved, as the function might behave differently on either side of a given point.

Diketahui fungsi f(x) = |2x - 4| / (2 - x). Berikut adalah pernyataan yang benar tentang limit dan nilai dari fungsi ini.

This problem explores the limit behavior and continuity of the function f(x) = |2x - 4| / (2 - x). Learn how to calculate limits approaching x = 2 from the left and right, and understand the impact of absolute value on continuity. Suitable for students in Grades 10-12.

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