- #1
emma83
- 33
- 0
Homework Statement
Find the inverse function [tex]f^{-1}[/tex] of the binary entropy [tex]f[/tex] (given below) on the domain of definition [0;1/2[ (i.e. where [tex]f[/tex] is continuous strictly increasing).
The function [tex]f[/tex] is given by:
[tex]f(x)=-x\log(x)-(1-x)\log(1-x)[/tex]
(where [tex]\log[/tex] is the logarithm base 2)
Homework Equations
If I am right with the calculation, this is equivalent to solving:
[tex]x^{x}(1-x)^{1-x}=2^{-y}[/tex]
But I have no clue how to solve this either!
The Attempt at a Solution
I don't know how to solve this, I also tried with computer programs such as Maple and Mathematica but was not able to compute it either (I don't know much of them so I guess this should be possible (?))