2025-01-20 03:41
from f(10)=14, f(20)=40,
f(xy) = f(x) + f(y).
f(20) = f(2)+f(10)
=f(2)+14=40.
then f(2)=40-14=26
f(10) = f(2)+f(5)
= 26+f(5) = 14
then
f(5) = 14-26 = -12
therefore
f(500) = f(5) + f(100)
= f(5) + f(10) + f(10)
= f(5) + 2f(10)
= -12+2×14 = -12+28
= 16