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
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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) ]
=4/3-1
=1/3
所以f[log3(3/4)]=-1/3
f[log1/3(36)]=-1/3
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) ]
=4/3-1
=1/3
所以f[log3(3/4)]=-1/3
f[log1/3(36)]=-1/3
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