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For $a,b \in \mathbb{R}$ with $a<b$, find an explicit bijection of $A=\{x: a < x < b\}$ onto $B=\{y: 0<y<1 \}$

Can someone please help? I don't understand what is meant by 'explicit'. Would sinx, cosx or tanx classify?

W_D
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user93729
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    Sorry! Is it visible now? – user93729 Sep 08 '13 at 11:15
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    'explicit' just means that you should write a concrete formula for the mappinmg function (and possibly its inverse) instead of e.g. merely showing the existence of such a bijection or describing a process that would provably result in such a bijection – Hagen von Eitzen Sep 08 '13 at 12:00

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Hint:

$$\begin{align*}g:(0,1)\to (a,b)&\;,\;\;g(x):=bx+(1-x)a=(b-a)x+a\\{}\\ f:(a,b)\to (0,1)&\;,\;\;f(x):=\frac{x-a}{b-a}\end{align*}$$

What's the relation between the functions $\;f,g\;$ ?

DonAntonio
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