Suppose that f : C → C is continuous on all of C. Suppose that f(1) = 1. Prove that there exists r > 0 such that if z ∈ D(1; r), then |f(z)| < 2. Hint: |f(z)| = |f(z) − 1 + 1

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A: According to the given information,

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A: See the attachment

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A: If part:

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