Hello,

I'm looking for a injective function defined as f: [0,1]-->]0,1[.

How should I start?

I'm trying to start with what it implies:

f:A--->B

A=[0,1]={x:0<=x<=1}

B=]0,1[={f(x):0<f(x)<1}

f(A)=B

x=y => f(x)=f(y) for all x,y in A.

It's not arctan(x) because im(arctan(x)) with x in[0,1] is not ]0,1[. So I rather think that f is only injective in [0,1].

I'm also thinking maybe I need to find f(x)^-1 first and then f(x), (since f is injective).

Thanks in advance!