Let g(x)=∫_0^x f( t ) dt, where f is continuous function in [0,3] such that 1/3 ≤ f( t ) ≤ 1 for all t ∈[0,1] and 0 ≤ f( t ) ≤ 1/2 for all t ∈(1,3].…

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