Find all functions f defined on non-negative real numbers having the following properties:
(i) For all non-negative x it is f(x)≥0.
(ii) It is f\left(1\right)\equal{}\frac 12.
(iii) For all non-negative numbers x,y it is f\left( y \cdot f(x) \right) \cdot f(x) \equal{} f(x\plus{}y). functionalgebra proposedalgebra