Let f : ℂ → ℂ be an analytic function. For z 0 ∈ ℂ, which of the following statements is true?

f(r) = z 0 for all r ∈ ℚ ∩ [1, 2] ⇒ f is the constant function z 0

f(n) = z 0 for all n ∈ ℕ ⇒ f is the constant function z 0

f can take the value z 0 at finitely many points in {1/n | n ∈ ℕ}

Let f : ℂ → ℂ be an analytic function. For z 0 ∈ ℂ, which of the following statements is true?

f(r) = z 0 for all r ∈ ℚ ∩ [1, 2] ⇒ f is the constant function z 0

f(n) = z 0 for all n ∈ ℕ ⇒ f is the constant function z 0

f can take the value z 0 at finitely many points in {1/n | n ∈ ℕ}

Let f : ℂ → ℂ be an analytic function. For z 0 ∈ ℂ, which of the... | Mathematics MCQ [Updated November 2026] | GkGet

Mathematics · Complex Analysis

Let f : ℂ → ℂ be an analytic function. For z₀ ∈ ℂ, which of the following statements is true?

Verified Solution4 OptionsUpdated: October 2026👁️1 View

1f(r) = z 0 for all r ∈ ℚ ∩ [1, 2] ⇒ f is the constant function z 0
2f(n) = z 0 for all n ∈ ℕ ⇒ f is the constant function z 0
3f(1/n) = z 0 for all n ∈ ℕ ⇒ f is the constant function z 0✓
4f can take the value z 0 at finitely many points in {1/n | n ∈ ℕ}

Correct answer

f(1/n) = z 0 for all n ∈ ℕ ⇒ f is the constant function z 0

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