四个函数 ①y=(x-1)平方 ②y=(1/2)*2的x次方 ③y=lg(x-1) ④y=cos平方∏（这是pai）x
2个回答
对于①f(x)=(x-1)^2
f(x1x2+1)=(x1x2)^2
[f(x1+1)]^x2=x1^x2不满足f(x1x2+1)=[f(x1+1)]
f(x+1/2)=(x-1/2)^2
1-f(x)=1-(x-1)^2不满足f(x+(1/2))=1-f(x)
对于②y=(1/2)*2^x
即f(x)=2^(x-1)
f(x1x2+1)=2^(x1x2)
[f(x1+1)]^x2=(2^x1)^x2=2^(x1x2)满足f(x1x2+1)=[f(x1+1)]
f(x+1/2)=2^(x-1/2)
1-f(x)=1-2^x不满足f(x+(1/2))=1-f(x)
对于 ③y=lg(x-1)
f(x1x2+1)=lg(x1x2)
[f(x1+1)]^x2=(lgx1)^x2不满足f(x1x2+1)=[f(x1+1)]
f(x+1/2)=lg(x-1/2)
1-f(x)=1-logx不满足f(x+(1/2))=1-f(x)
对于④y=(cosπx)^2
f(x1x2+1)=[cosπ(x1x2+1)]^2
[f(x1+1)]^x2=[cosπ(x1+1)]^2x2不满足f(x1x2+1)=[f(x1+1)]
f(x+1/2)=[cosπ(x+1/2)]^2=(sinπx)^2
1-f(x)=1-(cosπx)^2=(sinπx)^2满足f(x+(1/2))=1-f(x)
(1) ②
(2) ④
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