Question 912016
You might be asking for f^(-1)(x).


{{{(y-1)/(y+1)=x}}} using y as {{{f^(-1)(x)}}}.


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


{{{y-1=xy+x}}}


{{{y-xy=1+x}}}


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


{{{highlight(y=(x+1)/(1-x))}}}
{{{x<>1}}}
and you must check behavior to the left of -1, between -1 and +1, and to the right of +1.


{{{graph(300,300,-5,5,-5,5,(x+1)/(1-x))}}}