C3 Functions

http://www.madasmaths.com/archive/iygb_practice_papers/c3_practice_papers/c3_f.pdf

Need help in part 8(c), how do we get the range over here as 0<f(x)<4? I tend to get confused when finding the range and domain of such situations. Could anyone tell me how to do so? TIA.

Draw a graph?
For x > 1, the denominator is increasing as x increases, so f(x) is decreasing.
As x tends to infinity, f(x) gets smaller and closer to zero.
Then evaluate f(1).

So, you simply substituted x=1? Or you came to a conclusion by drawing out a graph?

Yes, substitution. Look at the graph, you don't even need to draw it. x>1 shows that you can ignore the left branch of it and since it is beyond the asymptote, the range will not involve infinity. So you can plug in x=1 and it will be everything between (and excluding including) f(1) and 0.