Let $$f: \mathbb{R} \to \mathbb{R}$$ be such that $$f(xy) = f(x)f(y)$$, for all $$x, y \in \mathbb{R}$$ and $$f(0) \ne 0$$. Let $$g: [1, \infty) \to \mathbb{R}$$ be a differentiable function such that $$$x^2 g(x) = \int_1^x (t^2 f(t) - tg(t))\,dt.$$$ Then $$g(2)$$ is equal to :

A

$$\dfrac{13}{8}$$

B

$$\dfrac{11}{16}$$

C

$$\dfrac{15}{32}$$

D

$$\dfrac{17}{64}$$