Mathematics · Real Analysis
Let f : [0, ∞) &to; [0, ∞) be a continuous function such that f(x+y) = f(x) + f(y) ∀ x, y ≥ 0, then:
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1f is not continuous at all irrational points
- 2f(x) = ax, ∀ x ≥ 0 for some non-zero constant a✓
- 3f is not monotone
- 4f is continuous only at x = 0
Correct answer
f(x) = ax, ∀ x ≥ 0 for some non-zero constant a
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