Mathematics · Complex Analysis

Let &mathbb;D = {z &in; &mathbb;C : |z| < 1} be the open unit disc and let f : &mathbb;D → &mathbb;D be a holomorphic function. Suppose that f(0) = 0 and f'(0) = 0. Which of the following is a possible value of f(1/2)?

Verified Solution4 OptionsUpdated: October 2026👁️1 View

1-1/2
21/2
3-1/4✓
41/3

Correct answer

-1/4

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Let &mathbb;D = {z &in; &mathbb;C : |z| < 1} be the open unit disc and let f : &mathbb;D → &mathbb;D be a holomorphic function. Suppose that f(0) = 0 and f'(0) = 0. Which of the following is a possible value of f(1/2)?

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Let &mathbb;D = {z &in; &mathbb;C : |z| < 1} be the open unit disc and let f : &mathbb;D &rarr; &mathbb;D be a holomorphic function. Suppose that f(0) = 0 and f'(0) = 0. Which of the following is a possible value of f(1/2)?

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Let &mathbb;D = {z &in; &mathbb;C : |z| < 1} be the open unit disc and let f : &mathbb;D → &mathbb;D be a holomorphic function. Suppose that f(0) = 0 and f'(0) = 0. Which of the following is a possible value of f(1/2)?