# Inverse of s(x)=[1+f(x)]/[1-f(x)]

1. Oct 28, 2012

### caitlinbennet

f is a one to one function with inverse f^-1, and we are asked to find the inverse of s(x)=[1+f(x)]/[1-f(x)]

My attempts leave me with s^-1(x)= [f^-1(1-x)]/[f^-1(-x-1)] and I don't think this is correct. I can't find any examples of problems like this online.

2. Oct 28, 2012

### tiny-tim

welcome to pf!

hi caitlinbennet! welcome to pf!

(try using the X2 button just above the Reply box )
so f(x) = … ?

and what does that tell you about s-1 ?

3. Oct 28, 2012

### caitlinbennet

Re: welcome to pf!

Is s-1 a composition of f-1.. I'm definitely missing something silly here...

4. Oct 28, 2012

### tiny-tim

f(x) = … ?

5. Oct 28, 2012

### caitlinbennet

(1+s(x))/1-s(x)?

6. Oct 28, 2012

### caitlinbennet

really have no idea where to start..

7. Oct 29, 2012

### caitlinbennet

I found the answer on wolfram alpha, I can invert normal functions but this one has me totally stumped.

8. Oct 29, 2012

### tiny-tim

hi caitlinbennet!

(just got up :zzz:)
ok, so suppose s(y) = x

then y = s-1(x), and y = f-1(f(y)) = … ?

9. Oct 29, 2012

### caitlinbennet

f(x)?

10. Oct 29, 2012

### tiny-tim

i mean, in terms of s(y) ?