Question

Let f(x) = x/(x-5). Find a function y = g(x) so that
(f o g)(x) = 2x.

Answer 1

\[f(g(x))=2x\]\[f(g(x))=\frac{ g(x) }{ g(x)-5 }\]\[\frac{ g(x) }{ g(x)-5 }=2x\]\[g(x)=2x g(x)-10x\]\[(2x-1)g(x)=10x\]\[g(x)=\frac{ 10x }{ 2x-1 }\]

Answer 2

Thank you very much...