Question

Найти f(x) если f((3x-1)/(x-2))= (x-1)/(x+1).

Answer 1

$f(\frac{3x-1}{x-2})=\frac{x-1}{x+1}\\ \frac{3x-1}{x-2}=t\\ 3x-1=tx-2t\\ x(3-t)=1-2t\\ x=\frac{1-2t}{3-t}\\ f(t)=\frac{\frac{1-2t}{3-t}-1}{\frac{1-2t}{3-t}+1} = \frac{t+2}{3t-4}\\\\ f(x)=\frac{x+2}{3x-4}$