Let \(f:R\to R\) be such that \(f(xy)=f(x)f(y)\), for all \(x,y\in R\) and \(f(0)\neq 0\). Let \(g:[1,\infty )\to R\) be…

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

[JEE Main 2026, 6 Apr (Shift 2)]