Question 54
Determine all functions $f:[0, \infty) \rightarrow \mathbb{R}$ such that $f(0)=0$ and
$$
f(x)=1+5 f\left(\left\lfloor\frac{x}{2}\right\rfloor\right)-6 f\left(\left\lfloor\frac{x}{4}\right\rfloor\right)
$$
for all $x\gt 0$.
$$
f(x)=1+5 f\left(\left\lfloor\frac{x}{2}\right\rfloor\right)-6 f\left(\left\lfloor\frac{x}{4}\right\rfloor\right)
$$
for all $x\gt 0$.