thanks
i think the biggest problem is that function is not well defined.
$\displaystyle f(1/2)=2\cdot 1 + 2=4$ but
$\displaystyle f(2/4)=2 \cdot 2 + 4= 8$
Even if it were well defined, its not injective
$\displaystyle f(3/4)=f(1/8)$ but clearly $\displaystyle 3/4 \not = 1/8$