The given function is:

$f(x) = \frac{2x - 4}{2 - x}$

Now, let's analyze the statements to determine which are correct.

Step 1: Simplify the function

We can simplify $f(x)$:

$f(x) = \frac{2(x - 2)}{2 - x}$

Notice that $2 - x$ can be written as $-(x - 2)$, so:

$f(x) = \frac{2(x - 2)}{-(x - 2)} = -2 \quad \text{for} \quad x \neq 2$

Thus, for all $x \neq 2$, $f(x) = -2$.

Step 2: Determine if $f(2)$ exists

At $x = 2$, the denominator becomes zero:

$f(2) = \frac{2(2) - 4}{2 - 2} = \frac{0}{0}$

Since we have an indeterminate form $\frac{0}{0}$, $f(2)$ is undefined.

Step 3: Evaluate limits around $x = 2$

1. Limit as $x \to 2^-$:

   • As $x \to 2$ from the left, $f(x) = -2$.

2. Limit as $x \to 2^+$:

   • As $x \to 2$ from the right, $f(x) = -2$.

Thus, $\lim_{x \to 2} f(x) = -2$.

Step 4: Analyze the statements

• a. Nilai $f(2)$ tidak ada (The value $f(2)$ does not exist): True. As shown, $f(2)$ is undefined.
• b. $\lim_{x \to 2} f(x) = 2$: False. The correct limit is $-2$, not 2.
• c. $\lim_{x \to 2^+} f(x) = -2$: True. The limit from the right is indeed $-2$.
• d. \lim_{x \to 2} f(x) tidak ada (The limit as \( x \to 2 does not exist): False. The limit exists and equals $-2$.
• e. $\lim_{x \to 2^-} f(x) = -2$: True. The limit from the left is also $-2$.

Conclusion

The correct statements are: a, c, and e.

Would you like a further explanation or have any specific questions?

Here are some related questions you might find useful:

1. How do you determine limits of a function at a point?
2. What is the meaning of a limit from the left or right?
3. How do you handle indeterminate forms like $\frac{0}{0}$?
4. Why do we say a function is undefined at a point?
5. What happens when the limit exists, but the function is undefined?

Tip: Always check the behavior of a function from both sides of a point to confirm whether the limit exists.