Part CCSIR NET December 2024omitting-a-disc-invites-liouville-on-the-reciprocal

Omitting a disc invites liouville on the reciprocal

Let $f : C$ \ {−1, 1} $\to C$ be a holomorphic function that does not take any value in the set { $z \in C$ : |z − 1| < 1}. Which of the following statements are true?

A.f is constant.✓
B.f has removable singularities at −1 and 1.✓
C.f is bounded.✓
D.f has either poles or essential singularities at −1 and 1.

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

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Omitting a disc invites liouville on the reciprocal

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