Mathematics · Real Analysis
Let g(x) be defined on the interval [0,1] by g(x) = x if x is rational, and g(x) = 0 if x is irrational. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1g(x) is unbounded on [0,1].
- 2g(x) is discontinuous on (0,1] and not Riemann Integrable.✓
- 3g(x) is Riemann Integrable.
- 4g(x) is continuous on (0,1] and not Riemann Integrable.
Correct answer
g(x) is discontinuous on (0,1] and not Riemann Integrable.
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