已知奇函数f(x)满足f(x+1.5)=f(x-1.5),当x属于(0,1)时,f(x)=3^x-1,求f(log1/3(36))的值

问题描述:

已知奇函数f(x)满足f(x+1.5)=f(x-1.5),当x属于(0,1)时,f(x)=3^x-1,求f(log1/3(36))的值

解f(x+1.5)=f(x-1.5),则f(x)=f(x-3)f[log1/3(36)]=f[log1/3(36)-3]=f[log1/3(36/27)]=f[log1/3(4/3)]=f[log3(3/4)]f(x)是奇函数,所以-f[log3(3/4)]=f[-log3(3/4)]=f[log3(4/3)] [log3(4/3)属于(0,1) ]=...