Q13/103) Given f(x) = x -3 for x >= 1000 and f(f(x+5)) x < 1000 find f(84)

we evaluate f(999) through f(995)

f(999) = 998
f(998) = 997
f(997) = 998
f(996) = 997
f(995) = 998

now f(85)= f^184 (999) = f^183( 998) notation for f is applied 183 times

applying f twice gives 998 and so on applying 182 time gives 998 and then once more gives 997 which is the ans

for some discussions refer to http://mathhelpboards.com/challenge-questions-puzzles-28/find-f-84-a-6600.html#post30091