Question

已知f(x)= (1/2)^x，x≥4； f(x+1), x＜4. 则f(log2³）=——————

已知f(x)= (1/2)^x，x≥4；
f(x)= f(x+1), x＜4. 则f(log2³）就是[以2为底3的对数]=——————

Answer 1

1<log2³<2，所以f(log2³）=f(log2³+1）=f(log2³+2）=f(log2³+3）=f(log2³+log2[8]）=f(log2[24]）又因为
log2[24]=log2³+3>4，所以f(log2[24]）=(1/2)^{log2[24]}=-24

注：一、(1/2)^x=2^(-x)
二、log2[8]是以2为底8的对数

Answer 2

f(log2 3)=f(log2 3 +1)

Answer 3

log2³<4
f(log2³）=f(log2³+1）
log2³+1=log2(6)<4
f(log2(6)）=f(log2(6)+1）
log2(6)+1=log2(12)<4=log2(16)
f(log2(12）=f(log2(12)+1）
log2(12)+1=log2(24)>4
f(log2(24）=(1/2)^log2(24)=1/24
即
f(log2³）=1/24

Answer 4

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