I would like to rearrange the logistic function:
$y=\frac1{1+\exp(-a+bx)}$
To calculate $x=f(y)$
So I did the following:
$\frac1{y}=1+\exp(-a+bx)$ $\ln\left(\frac1{y}-1\right)=-a+bx$ $\frac{\ln\left(\frac1{y}-1\right) +a}{b}=x$
but when I try to plot this function, it appears that I have lost a '-' somewhere, i.e., I have calculated $-x=f(y)$
Where I have missed the negative sign?