Question 768512
{{{f(x) = (2x-1)/x+3}}}


what is g(x) so that {{{g(f(x))=f(g(x))=(2(g(x))-1)/(g(x))+3=x}}}
{{{(2(g(x))-1)/(g(x))+3=x}}}
{{{2*g(x)-1=x(g(x)+3)}}}
{{{2*g(x)-1=x*g(x)+3x}}}
{{{2g(x)-x*g(x)=3x+1}}}
{{{g(x)(2-x)=3x+1}}}
This should be the inverse: {{{highlight(g(x)=(3x+1)/(2-x))}}}


Just BE AWARE, this IS IMPERFECT BECAUSE f(x) has a asymptote at x=0, but g(x) is defined at g(x)=0.  Also f(x)=2 works for f(x) but g(x) is not defined for x=2.


f(x) {{{graph(300,300,-5,5,-15,15,(2x-1)/x+3)}}}


g(x) {{{graph(300,300,-5,5,-15,15,(3x+1)/(2-x) )}}}