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.