g(x) where 1/2f(t)1    ,t belongs to [0,1]     and 0f(t)1/2for t belongs (1/2], then

1)-3/2g(2)1/2

2)0g(2)2

3)3/2g(x)5/2

4)2g(2)4

We have,g(2)=.So,

For t in [0,1],1/2f(t)1 and so, 

Thus,1/21.

similarly,for t in [1,2],0f(t)1/2 and so,01/2.

Hence,1/2+01+1/2

So,1/2g(2)3/2 is the answer.

The best option that suits is [0,2) which is a super set of [1/2,3/2].Thus,the ans is option (B).