Question 1008364
Assuming that you really have  {{{f(x)=(5x-9)/(3x-7)}}},  because grouping properly is important,...


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


Using your definition for f, and letting input for f be g(x), you expect
{{{(5g(x)-9)/(3g(x)-7)=x}}}.
Solve for g(x).