Question 892069
Here is some help with the inverse part.


You likely are starting with {{{g(x)=5x/(x-9)}}}


You want to find {{{g^(-1)(x)}}}.
{{{5g^(-1)(x)/(g^(-1)(x)-9)=x}}}.
SOLVE THAT FOR {{{g^(-1)(x)}}}.


Let me use y instead of all that text...
{{{5y/(y-9)=x}}}
{{{5y=x(y-9)}}}
{{{5y=xy-9x}}}
{{{5y-xy=-9x}}}
{{{y(5-x)=-9x}}}
{{{y=-9x/(5-x)}}}
multiply by {{{(-1)/(-1)}}}
{{{highlight(y=9x/(x-5))}}}-----the inverse


DOMAIN:
All real numbers except that {{{x<>5}}}.
(-infinity,5) U (5,infinity)


RANGE:
You figure this!  What happens as x tends toward -infinity or toward infinity?
What happens to {{{g^(-1)}}} near x=5, on either sides?