question_answer

Let \[g\,\,(x)=\int_{0}^{x}{f\,\,(t)\,\,\,dt,}\] where f is such that \[\frac{1}{2}\,\,\underline{<}\,\,f\,\,(t)\,\,\underline{<}\,\,1\] for \[t\in [0,1]\] and \[0\,\,\underline{<}\,\,f\,\,(t)\,\,\frac{1}{2}\] for\[t\in [1,2]\]. Then g(2) satisfies the inequality:

A)  \[-\frac{3}{2}\,\,\underline{<}\,\,g\,\,(2)<\frac{1}{2}\]    

B)  \[0\underline{<}\,\,g\,\,(2)<2\]

C)  \[\frac{3}{2}\,\,\underline{<}\,\,g\,\,(2)<\frac{5}{2}\]     

D)  \[2\underline{<}\,\,g(2)<4\]

E)  None of these