Inverse functions

[iwfc87]

I know what inverse functions are, but how do I find an inverse of something like this:

 

y=(e^x)/(1+e^x).

 

What I thought of doing which I'm not sure about is:

 

y(1+e^x) = e^x

y+ye^x = e^x

(y/e^x)+y = 1

1/e^x +1 = 1/y

e^x = y-1

x = ln(y-1)

 

I think what I've done is ridiculously wrong..but yeah...

[ecoli]

inverse function - switch x and y then solve for y... I'm not so sure you did that.

[rakuenso]

here's what I did:

 

first switch x and y

 

[math]

x=e^y/(1+e^y)

[/math]

[math]

ln x = y - ln(1+e^y)

[/math]

[math]

ln x + ln (1+e^y) = y

[/math]

[math]

x + xe^y = e^y

[/math]

[math]

y = lnx - ln(1-x)

[/math]