Verify if the two functions are inverses by showing that f(g(x))=x\displaystyle {f{{\left({g{{\left({x}\right)}}}\right)}}}={x} and g(f(x))=x\displaystyle {g{{\left({f{{\left({x}\right)}}}\right)}}}={x}.

f(x)=1x79x+7\displaystyle {f{{\left({x}\right)}}}=\frac{{{1}{x}-{7}}}{{-{9}{x}+{7}}} g(x)=77x9x1\displaystyle {g{{\left({x}\right)}}}=\frac{{-{7}-{7}{x}}}{{-{9}{x}-{1}}}