Let \( g(x) = \displaystyle\int\limits_{0}^{x} f(t)\,dt \), where \( f \) is continuous function in \( [0,3] \) such that \( \dfrac{1}{3} \le f(t) \le 1 \) for all \( t \in [0,1] \) and \( 0 \le f(t) \le \dfrac{1}{2} \) for all \( t \in [1,3] \). The largest possible interval in which \( g(3) \) lies is:
