Because the first time-f (x) = 3 = 2 2-1.
Second time-f (x) = 7 = 2 3-1
The third time-f (x) =15 = 2 4-1.
The fourth time-f (x) = 31= 2 5-1.
See the law, for t time, the result is 2 (t+ 1)- 1.
So if the result is n, then solve equation 2 (t+ 1)- 1 = n to get the answer.