已知函数f(x)=(1/2)^x(x≥2),f(x)=f(x+1)(x<2) 则 f(log2(3))的值为

问题描述:

已知函数f(x)=(1/2)^x(x≥2),f(x)=f(x+1)(x<2) 则 f(log2(3))的值为

log3(3)所以原式=f[log2(3)+1]
=f[log2(6)]
log2(6)>2
所以原式=(1/2)^log2(6)
=2^[-log2(6)]
=2^[log2(1/6)]
=1/6