If f and g are monotonic, is f(g(x))?

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Homework Help Overview

The discussion revolves around the properties of monotonic functions, specifically whether the composition of two increasing functions, f and g, results in another increasing function, f(g(x)).

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to establish whether the composition of two increasing functions is also increasing and expresses uncertainty about how to prove this.

Discussion Status

Some participants have referenced previous discussions on the topic, indicating that there may be established insights or guidance available. There is acknowledgment of advice given, suggesting that the conversation is moving towards clarification of the concepts involved.

Contextual Notes

The original poster is seeking a proof or counterexample, which implies a need for rigorous reasoning within the constraints of the homework context.

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1. Homework Statement
If f and g are both increasing functions, is it true that f(g(x)) is also increasing? Either prove that it is true or five an example that proves it false.


2. Homework Equations



3. The Attempt at a Solution
I know that it is indeed also increasing, but I'm unsure how to prove it.
 
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Thanks for the help.
 
NWeid1 said:
Thanks for the help.

micromass's advice is quite good. Pay attention to it.
 

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