Question 8
(FRG 3) For all rational $x$ satisfying $0\le x\lt 1$, $f$ is defined by
$$f(x)=\begin{cases}f(2x)/4,&0\le x\lt 1/2,\\3/4+f(2x-1)/4,&1/2\le x\lt 1.\end{cases}$$
Given that $x=0.b_1b_2b_3\ldots$ is the binary representation of $x$, find $f(x)$.
$$f(x)=\begin{cases}f(2x)/4,&0\le x\lt 1/2,\\3/4+f(2x-1)/4,&1/2\le x\lt 1.\end{cases}$$
Given that $x=0.b_1b_2b_3\ldots$ is the binary representation of $x$, find $f(x)$.