Inverse Logistic Function / Inverse Sigmoid Function

I am currently encoding a fuzzy logic library in java. I found equations for all standard functions - Grade, inverseGrade, Triangle, Trapezoid, Gaussian. However, I cannot find the inverse of the sigmoid / logistic function.

As I wrote the logistic function, java:

//f(x) = 1/(1+e(-x))
public double logistic(double x){

   return (1/(1+(Math.exp(-x)));

}

But I can neither find nor find the inverse. My algebraic / calculus abilities are quite limited, so I could not handle the inverse function.

Any hints or pointers would be of great help.

thank

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1 answer

If

y = 1/(1+exp(-x))

then

x = ln(y/(1-y))
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