Question 906484
The given funcgtion,  {{{f(x) = (x-7)/x}}}


Let g(x) be the inverse of f(x).  This means {{{g(f(x))=f(g(x))=x}}}


Without staying with the fancy formal method, just switch f and x, but call the FUNCTION you
are looking for, as g.


{{{(g-7)/g=x}}}
{{{g-7=g*x}}}
{{{-7=g*x-g}}}
{{{g*x-g=-7}}}
{{{g(x-1)=-7}}}
{{{g=-7/(x-1)}}}
More formally although some of the formality was not used that way,
{{{highlight(f^-1(x)=-7/(x-1))}}}