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