Question 712297
We look for another function g(x) so that g(f(x))=f(g(x))=x.


Considering the given function f(x)=ln(8-x), use g(x) as input:
f(g(x))=ln(8-g(x))=x, because we want f and g to be inverses.


{{{ln(8-g(x))=x}}}
{{{e^x=8-g(x)}}}
{{{e^x-8=-g(x)}}}
{{{8-e^x=g(x)}}}
or
{{{g(x)=8-e^x}}},  the inverse of {{{f(x)=ln(8-x)}}}.


g(x)=8-e^x,  graph:
{{{graph(550,550,-20,20,-20,20,8-e^x)}}}