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Letf: [0, ∞)→ [0, ∞) and g: [0, ∞) → [0, ∞) be non-increasing and non-decreasing functions respectively, and h(x) = g(f(x)). If h(0) = 0. Then show h(x) is always identically zero.

Letf: [0, ∞)→ [0, ∞) and g: [0, ∞) → [0, ∞) be non-increasing and non-decreasing functions respectively, and h(x) = g(f(x)). If h(0) = 0. Then show h(x) is always identically zero.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 1CR
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Let/: [0, ∞)[0, ∞) and g: [0, ∞) [0, ∞) be non-increasing and non-decreasing functions respectively, and h(x) = g(f(x)) Ifk(0) = 0 Then show h(x) is always identically zero.

 

Letf: [0, ∞)→ [0, ∞) and g: [0, ∞) → [0, ∞) be non-increasing and non-decreasing functions respectively, and h(x) = g(f(x)). If h(0) = 0. Then show h(x) is always identically zero.
Transcribed Image Text:Letf: [0, ∞)→ [0, ∞) and g: [0, ∞) → [0, ∞) be non-increasing and non-decreasing functions respectively, and h(x) = g(f(x)). If h(0) = 0. Then show h(x) is always identically zero.
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