# Math Help - sigmoid function

1. ## sigmoid function

hi,
I have some problem with the proof of the following problem

sigmoid function ( $r(s)= 1/(1+e^-^s)$)
is antisymetric about the point (0,1/2)

2. Originally Posted by EITP
hi,
I have some problem with the proof of the following problem

sigmoid function ( $r(s)= 1/(1+e^-^s)$)
is antisymetric about the point (0,1/2)

Anti-symmetric about $(0,1/2)$ means that $t(s)=r(s)-1/2$ is anti-symmetric, that is:

$
t(s)=-t(-s)
$

Now:

$
t(s)=\frac{1}{1+e^{-s}}-\frac{1}{2}=\frac{1-e^{-s}}{2(1+e^{-s})}
$
.

Now multiply both top and bottom of the LHS by $e^{s}$:

$
t(s)=\frac{e^s-1}{2(e^s+1)}=-t(-s)
$

QED

RonL