Let $g(n)$ is a continuous differential function which takes positive value for $x \leq 0$ and satisfy $\int \limits_0^2 g(t) dt = x \sqrt {g(x)}$ with $f(1) =V_2$. find the value of $f(\sqrt 2 +1)$

Question

$(a)\;\frac{1}{4} \\ (b)\;4 \\ (c)\;\sqrt 2 +1 \\ (d)\;\sqrt 2 -1$