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

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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.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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