Question

高一数学题,对于任意x,[x]为不超过x的最大整数,如[1.1]=1,[-2.1]=-3,定义R上的函数f(x)=[2x

Answer 1

0 ≤ x ≤ 1

当x = 1时,f(x) = 14

当7/8 ≤ x < 1时,

7/4 ≤ 2x < 2,7/2 ≤ x < 4,7 ≤ 8x < 8

f(x) = 1 + 3 + 7 = 11

当3/4 ≤ x < 7/8时

3/2 ≤ 2x < 7/4,3 ≤ x < 7/2,6 ≤ 8x < 7

f(x) = 1 + 3 + 6 =10

下面类似讨论有

当5/8 ≤ x < 3/4时,f(x) = 1 + 2 + 5 = 8

当1/2 ≤ x < 5/8时,f(x) = 1 + 2 + 4 = 7

当3/8 ≤ x < 1/2时,f(x) = 0 + 1 + 3 = 4

当1/4 ≤ x < 3/8时,f(x) = 0 + 1 + 2 = 3

当1/8 ≤ x < 1/4时,f(x) = 0 + 0 + 1 = 1

当0 ≤ x < 1/8时,f(x) = 0 + 0 + 0 = 0