设函数f1(x)=x^1/2,f2(x)=x^-1,f3(x)=x^2,则f3(f2(f1(2011)))=?
问题描述：
设函数f1(x)=x^1/2,f2(x)=x^-1,f3(x)=x^2,则f3(f2(f1(2011)))=?
答
f1(2011)=(2011)^1/2=根号2011
f2(f1(2011))=(根号2011)^-1=1/根号2011
f3(f2(f1(2011)))=(1/根号2011)^2=1/2011
答
因为f1(x)=x^1/2
所以f1(2011)=2011^(1/2),f2(f1(2011))=f2(2011^(1/2))
因为f2(x)=x^(-1)
所以f2(f1(2011))
=f2(2011^(1/2))
=2011^(-1/2),
f3(f2(f1(2011)))=f3(2011^(-1/2))
因为f3(x)=x^2,
所以f3(f2(f1(2011)))=f3(2011^(-1/2))=[2011^(-1/2)]^2=2011^(-1)=1/2011