Question 938600
Not sure what you really have to start with,
you want the inverse of f(x)=(1/x+2)-1  or  when rendered, {{{f(x)=(1/x+2)-1}}}.


Let g(x) be the inverse of f.
{{{g(f(x))=f(g(x))=x}}}---meaning of the inverse of a function
{{{1/(g(x)+2)-1=x}}}---using g as the input of f
{{{1/(g(x+2))=x+1}}}
{{{1=(g(x)+2)(x+1)}}}
{{{x*g(x)+2x+g(x)+2=1}}}
{{{x*g(x)+g(x)+2x=1}}}
{{{x*g(x)+g(x)=1-2x}}}
{{{(x+1)g(x)=1-2x}}}
{{{highlight(g(x)=(1-2x)/(x+1))}}}