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Part BCSIR NET December 2025match-taylor-coefficients-in-order-each-one-is-forced-to-zero-in-turn

Match taylor coefficients in order each one is forced to zero in turn

Let 𝔻 denote the open unit disc {z∈Cz \in \mathbb{C} : |z| < 1} and X = {f : 𝔻 β†’C\to \mathbb{C} ∣ f is holomorphic and satisfies f(2z)=f(z)/(1βˆ’f(z)2)f(2z) = f(z)/(1 - f(z)^{2}) for all |z| < 1/2}. Which of the following statements is true?

  1. A.X is uncountable.
  2. B.X is infinite and countable.
  3. C.Every element of X is an open map.
  4. D.X has exactly one element.βœ“

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

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

See pricing

50 are analysed free β€” try those first.

Related counterexample: Zeros of a non-constant holomorphic function cannot accumulate

More on this topic

The chapter behind this: Analyticity, the identity theorem and zeros β€” free to read

From Analytic Functions β€Ί Power series and analyticity

Last revised . Found a mistake? Tell us β€” corrections are the fastest thing we act on.

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