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Jan
4
awarded  Scholar
Jan
4
accepted Looking for a magnifyer function
Jan
4
accepted Inverse function
Jan
4
comment Inverse function
Thanks! wolframalpha formula looks great.
Jan
4
revised Inverse function
added 3 characters in body
Jan
4
comment Inverse function
$\alpha$ is within $]0,3[$
Jan
4
comment Inverse function
The domain is $[0,1]$. $\alpha$ is smaller than 3, which ensure the bijection on $[0,1]$.
Jan
4
revised Inverse function
added 11 characters in body
Jan
4
asked Inverse function
Jan
4
comment Looking for a magnifyer function
Thanks Didier. Are you sure the inverse function is correct?
Jan
1
revised Looking for a magnifyer function
added 4 characters in body
Jan
1
comment Looking for a magnifyer function
Thanks andré, you are right: the last condition is incompatible. I replace it with: $\lim\limits_{x\to0} f'(x)=+\infty$
Jan
1
awarded  Editor
Jan
1
comment Looking for a magnifyer function
oops, I did a mistake in my last requirement: it is $x f'(x)$ and not $x f(x)$. Sorry.
Jan
1
revised Looking for a magnifyer function
error in last requirement
Dec
31
comment Looking for a magnifyer function
@Thomas yes, my last requirement is what you have written. And, f has to be continuous on [0,1]
Dec
31
asked Looking for a magnifyer function
Dec
31
awarded  Supporter
Aug
10
awarded  Autobiographer