Mathematics · Real Analysis
Let f : (0, ∞) → (0, ∞) be a uniformly continuous function. Define g : (0, ∞) → (0, ∞) by g(x) = x2 if 0 1. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Both f ˆ g and g ˆ f are uniformly continuous.✓
- 2Neither f ˆ g nor g ˆ f is uniformly continuous.
- 3g ˆ f is uniformly continuous, but f ˆ g is not uniformly continuous.
- 4f ˆ g is uniformly continuous, but g ˆ f is not uniformly continuous.
Correct answer
Both f ˆ g and g ˆ f are uniformly continuous.
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