MathNet 2014 Question 55

Let $a \in (0, 1)$. Find all functions $f : \mathbb{R} \to (0, \infty)$ so that $f(x) \le a^x$ and $f(x + y + z) \le f(x)f(y)f(z)$, for every $x, y, z \in \mathbb{R}$.