Let f:RβR f : \mathbb{R} \to \mathbb{R} f:RβR be a twice differentiable function such that f(x+y)=f(x)f(y) f(x + y) = f(x) f(y) f(x+y)=f(x)f(y) for all x,yβR x, y \in \mathbb{R} x,yβR. If fβ²(0)=4a f'(0) = 4a fβ²(0)=4a and f f f satisfies fβ²β²(x)β3afβ²(x)βf(x)=0 f''(x) - 3a f'(x) - f(x) = 0 fβ²β²(x)β3afβ²(x)βf(x)=0, where a>0 a > 0 a>0, then the area of the region R = {(x, y) | 0 β€\leqβ€ y β€\leqβ€ f(ax), 0 β€\leqβ€ x β€\leqβ€ 2\ is :