How can I prove it? (injection, bijection, surjection)

gotmejerry
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Homework Statement


How can I prove this?

If g°f is a bijective function, then g is surjective and f is injective.

Homework Equations





The Attempt at a Solution

 
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First what does g°f mean
what does bijective mean
what does surjective mean
what does injective mean
 
Start of with let g of f be a bijection, than state of the definition of a bijection. From there you can prove what must be true of g and f for g of f to meet the definition.
 
I can see why it is need to be true, when I draw it, unfotunately I cannot write down the solution in a mathematical way.
 
To start say
Let g°f be a bijective function.

then what can you say about g°f
 

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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