Mathematics · Calculus

The Dirichlet function f: R → R defined as f(x) = 1 if x is rational and f(x) = -1 if x is irrational, is:

Verified Solution4 OptionsUpdated: October 2026👁️1 View

1discontinuous for every x ∈ R✓
2continuous at x = 0
3continuous at irrational points
4continuous at rational points

Correct answer

discontinuous for every x ∈ R

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The Dirichlet function f: R → R defined as f(x) = 1 if x is rational and f(x) = -1 if x is irrational, is:

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The Dirichlet function f: R → R defined as f(x) = 1 if x is rational and f(x) = -1 if x is irrational, is:

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