Question

设f(x)在[0,1]上为非减函数,且满足下列三个条件f(0)=0;f(x/5)=0.5f(x);f(x)=2-f(1-

Answer 1

f(0)=0;f(x/5)=0.5f(x);f(x)=2-f(1-x),

f(1)=2-f(0)=2,

f(1/2)=2-f(1/2)==> f(1/2)=1

f(1/5)=0.5*f(1)=1

f(1/25)=0.5*f(1/5)=1/2

f(1/125)=1/4

f(1/625)=1/8

f(1/3025)=1/16

f(1/2)=1

f(1/10)=1/2

f(1/50)=1/4

f(1/250)=1/8

f(1/1250)=1/16

∵f(x)在[0,1]上为非减函数

∴f(1/1250)≥f(1/2012)≥f(1/3025)

∴1/16≥f(1/2012)≥1/16

∴f(1/2012)=1/16=0.0625

选C