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The question provided is in Indonesian and asks to determine whether the function

\[
f(x) = \frac{20 - 10x}{x - 2}
\]

is continuous at \( x = 2 \). Let's analyze the function's continuity at \( x = 2 \).

### Step-by-Step Analysis:

1. **Check the function's definition**:
   The function \( f(x) = \frac{20 - 10x}{x - 2} \) appears to have a potential problem at \( x = 2 \) because it would result in a division by zero (since the denominator becomes zero at \( x = 2 \)).

2. **Simplify the expression**:
   Let's try to factor the numerator to see if it cancels out the denominator. The numerator \( 20 - 10x \) can be factored as:
   \[
   20 - 10x = -10(x - 2)
   \]
   So the function becomes:
   \[
   f(x) = \frac{-10(x - 2)}{x - 2}
   \]
   For \( x \neq 2 \), we can cancel out the \( (x - 2) \) terms:
   \[
   f(x) = -10 \quad \text{for} \quad x \neq 2
   \]

3. **Check the limit**:
   The simplified form of the function \( f(x) = -10 \) suggests that for any \( x \) near 2 (but not equal to 2), the function approaches \( -10 \).

4. **Evaluate at \( x = 2 \)**:
   However, at \( x = 2 \), the function is not defined (since the original form has a zero in the denominator). So, the function has a **removable discontinuity** at \( x = 2 \).

5. **Conclusion**:
   The function is not continuous at \( x = 2 \) because it is not defined there, but the discontinuity is removable. By defining \( f(2) = -10 \), the function would become continuous.

---

Would you like more details on any specific part of this explanation?

### Related Questions:
1. What is a removable discontinuity?
2. How do we determine if a function is continuous at a point?
3. What happens when the denominator of a function becomes zero at a specific point?
4. How do limits help in determining continuity?
5. Can we redefine a function to make it continuous?

**Tip**: Always check the behavior of a function near the point where it might be discontinuous by factoring and simplifying expressions.

Tentukanlah, apakah fungsi f(x) = (20 - 10x) / (x - 2) kontinyu pada x = 2? Jelaskan jawaban saudara.

Learn how to determine if the function f(x) = (20 - 10x) / (x - 2) is continuous at x = 2 with a detailed step-by-step explanation. This problem explores the concepts of limits, factoring, and removable discontinuity, suitable for students in Grades 11-12.

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