Chefs Favourite Function

Chef's new friend hErd gave him two functions $f$ and $g$. - The function $f$ is defined over $x$ $(x\geq 1)$ as: $$ f(x) = \begin{cases} 0, & \text{if } x = 1 \\ f\left( \frac{x}{2} \right) + 1, & \text{if } x \text{ is even} \\ f\left( \left\lfloor \frac{x}{2} \right\rfloor \right), & \text{if } x \text{ is odd} \\ \end{cases} $$ - The function $g$ is defined over $x$ $(x\geq 1)$ as: $$ g(