inverse of f(x)= (x-1)/(x+1)

Question

Finding inverse function  of f(x)=(x-1)/(x+1)

Answer 1

Are you looking for the inverse function of
f(x) = (x-1)/(x+1)
 
Or just the inverse of (x-1)/(x+1)
 
The inverse of (x-1)/(x+1) is 1/[(x-1)/(x+1)] = (x+1)/(x-1)
 
Note:  The inverse of x is 1/x

Answer 2

 

start with y =(x-1)(x+1)

 

replace x and y

 

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

 

x = y^2-1

 

x+1 = y^2

 

y = +- sqrt(x+1)

 

the inverse is not a function