Integral Calculus: JEE Main 2025 Mathematics question

Let $f: \mathbb{R} \to \mathbb{R}$ be a twice differentiable function such that $f(x + y) = f(x) f(y)$ for all $x, y \in \mathbb{R}$. If $f'(0) = 4a$ and $f$ satisfies $f''(x) - 3a f'(x) - f(x) = 0$, $a > 0$, then the area of the region $\mathbb{R} = \{(x, y) \mid 0 \leq y \leq f(a x), 0 \leq x \leq 2\}$ is: