Inverse Logistic Function / Reverse Sigmoid Function

Question

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

The way I have written the logistic function is java is :

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

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

}

But I can't work out or find the inverse anywhere. My algebraic/calculus abilities are fairly limited, hence why I haven't been able to work out the inverse of the function.

Any hints or pointers would be a big help.

Thanks

Answer 1

If

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

then

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