Let \(g(x)=\int_0^x f(t) d t\), where \(f\) is continuous function in \([0,3]\) such that \(\frac{1}{3} \leq f(t) \leq 1…

Let \(g(x)=\int_0^x f(t) d t\), where \(f\) is continuous function in \([0,3]\) such that \(\frac{1}{3} \leq f(t) \leq 1\) for all \(t \in[0,1]\) and \(0 \leq f(t) \leq \frac{1}{2}\) for all \(t \in(1,3]\). The largest possible interval in which \(g (3)\) lies is:

[JEE Main 2021, 18 Mar (Shift 2)]