Question

若函数f(x)=f(x+1)（x<4),f(x)=(0.5)^x(x≥4）,则f(log23)的值为

Answer 1

f(log23)=f(log23+1)=f(log26)
f(log26)=(log26+1)=f(log212)
f(log212)=f(log224)
f(log224)=(0.5)^log224=2^-log224=1/24

Answer 2

2<3<2²
∴1<log(2) 3<2
f(log(2)3)
=f(log(2)3+3)
=(0.5)^[(log(2)3+3)]
=(1/2)^[log(2) 3+log(2) 8]
=(1/2)^[log(2)24]
=(1/2)^[log(1/2)24]/[log(1/2)2]
=(1/2)^[-log(1/2)24]
=(1/2)^[log(1/2) 1/24]
=1/24