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Suppose f: (0, ∞) → (0, ∞) is a continuous function, and g: (0, ∞0)→ (0, ∞) is defined by the property that g(x) = (f(x))² for every positive real number *. True or false: If g is differentiable, then f must be differentiable too. True False

Suppose f: (0, ∞) → (0, ∞) is a continuous function, and g: (0, ∞0)→ (0, ∞) is defined by the property that g(x) = (f(x))² for every positive real number *. True or false: If g is differentiable, then f must be differentiable too. True False

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Suppose f: (0, ∞) → (0, ∞) is a continuous function, and g: (0, ∞) → (0,00) is defined by the property that g(x) = (f(x))² for every positive real number . True or false: If g is differentiable, then f must be differentiable too. True False
Transcribed Image Text:Suppose f: (0, ∞) → (0, ∞) is a continuous function, and g: (0, ∞) → (0,00) is defined by the property that g(x) = (f(x))² for every positive real number . True or false: If g is differentiable, then f must be differentiable too. True False
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