That is a very good start. I suggest that you continue by completing the square, to get You know that t must lie between 0 and 1, so from that you can work out the range of the function.
Sorry! I have done so, but not understanding whether i should put value of t here. If i do so answer is 1 in both cases. Help
You have to think about what happens as t goes from 0 to 1. As t goes from 0 to 1/2, goes from 1/4 down to 0. And as t goes from 1/2 to 1, goes from 0 back up to 1/4. So the range of will be the interval [0,1/4]. It follows that the range of is the interval [3/4,1].