Find all $f(x)$ such that $f(4x) + 2f(x+1) = \sqrt{x} + \sqrt{x+1}$, for all $x \ge 0$.

Question

A particular solution is: $f(x) = \frac{1}{2} \sqrt{x}$, obs: don't use this as a given, this is just to show that there is at least one solution.

What method should i use to solve this type of equation?