Assume that f (x) and g(x) are both differentiable functions on some interval I; in addition, assume that f(x) and g(x) are increasing on I. Let h(x) = f(g(x)). Show that h(x) is also increasing on I. (Note: This is a generalization of Q4, where you are not given a specific f or g.)
Assume that f (x) and g(x) are both differentiable functions on some interval I; in addition, assume that f(x) and g(x) are increasing on I. Let h(x) = f(g(x)). Show that h(x) is also increasing on I. (Note: This is a generalization of Q4, where you are not given a specific f or g.)
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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Transcribed Image Text:Assume that \( f(x) \) and \( g(x) \) are both differentiable functions on some interval \( I \); in addition, assume that \( f(x) \) and \( g(x) \) are increasing on \( I \).
Let \( h(x) = f(g(x)) \). Show that \( h(x) \) is also increasing on \( I \). (Note: This is a generalization of Q4, where you are not given a specific \( f \) or \( g \).)
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