Is the composition of two increasing functions also increasing?

[NWeid1]

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.

 

[Dick]

You already asked this. https://www.physicsforums.com/showthread.php?t=557158

 

[NWeid1]

Thanks for the help.

 

[Dick]

Thanks for the help.

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