Let Q^\plus{} denote the set of positive rational numbers. Show that there exists one and only one function f: Q^\plus{}\to Q^\plus{} satisfying the following conditions:
(i) If 0<q<1/2 then f(q)\equal{}1\plus{}f(q/(1\minus{}2q)),
(ii) If 1<q≤2 then f(q)\equal{}1\plus{}f(q\minus{}1),
(iii) f(q)\cdot f(1/q)\equal{}1 for all q\in Q^\plus{}. functioncontinued fractionalgebra proposedalgebra