Question 714843
This is not the exact formal way to look for the inverse but is usually easy, fast.


From given {{{f(x)=(2x)/(x+5)}}}, switch places of x and f(x), but call f(x) something else.


y=(2x)/(x+5), from that make, {{{x=2y/(y+5)}}} and try to solve for y.
{{{x(y+5)=2y}}}
{{{xy+5x=2y}}}
{{{xy-2y=-5x}}}
{{{y(x-2)=-5}}}
{{{highlight(y=(-5)/(x-2))}}}, but we should maybe call this, like g(x) as
{{{g(x)=(-5)/(x-2)}}} and say that g(x) and f(x) are inverses.