Limits of a Function

Question

Let  𝑓(𝑥)=ln(𝑥−1)2𝑥−4f(x)=ln⁡(x−1)2x−4 . Find the correct statement(s).

Choose all that apply.

Group of answer choices

1. 𝑓(2) does not exist.
2. 𝑓(2)=0.5
3. The point  (2,0.5) is on the graph of  𝑓 .
4. The graph of  𝑓 has a hole at  𝑥=2 .

Answer 1

For f(x) = ln(x-1)/(2x-4), f(2) does not exist (0 in denominator), and the graph has a hole at x = 2 since the limit as x goes to 2 does exist (and equals 1/2).