Can someone explain how you do this problem?
2006-10-06 06:16:02 · 4 answers · asked by hphgrwd 2 in Science & Mathematics ➔ Mathematics
If f(x) * f(f(x)) = 1 for every real number x, then for every number y in the range of f, y * f(y) = 1, and therefore f(y) = 1/ y.
Therefore, provided that 500 belongs to the range of f.
Now f(1000) = 999 proves that 999 is in the range of f. Therefore, f(999) = 1/999.
ASSUMING that the domain of f is connected, its continuity and the fact that 1/999 and 999 belong to its range imply that all numbers in between also belong to the range, in particular 500.
2006-10-06 10:38:22 · answer #1 · answered by dutch_prof 4 · 0⤊ 0⤋
I don't think both of those statements can be true.
f(x) * f(f(x)) = 1 implies that f(x) = 1/x
so f(1000) could not be 999
2006-10-06 14:36:57 · answer #2 · answered by Ken H 4 · 0⤊ 0⤋
fof(x)=1/f(x)
f(1000)=999
f(999)=1/f(1000)=1/999
===> f(x)=1/x
2006-10-06 13:35:41 · answer #3 · answered by Mohsen 1 · 0⤊ 2⤋
Do you know f(x)? Do you know its formula? Don't tell me. Do the f(500) yourself.
Ha HA
I don't think anyone would answer your problem, really a problem correctly.
2006-10-06 13:20:46 · answer #4 · answered by ? 2 · 0⤊ 2⤋