MathNet 2012 Question 37

Find a function $f : \mathbb{R}^{\ge 0} \to \mathbb{R}^{\ge 0}$ satisfying $f(2x + 1) = 4f(x) + 9$ for all $x \ge 0$. ($\mathbb{R}^{\ge 0}$ is the set of nonnegative real numbers.)