f(x)=2+log3 x
g(x)=[f(x)]^2+f(x^2)
=4+(log3 x)^2+4*(log3 x)+2+log3 (x^2)
=(log3 x)^2+4*(log3 x)+2*(log3 x)+6
=(log3 x)^2+6*(log3 x)+6
设t=log3 x,∵1≤x≤9 ∴t∈[0,2]
g(x)=(log3 x)^2+6*(log3 x)+6
=(t+3)^2-3
当t∈[0,2]时,g(x)是增函数
∴最小值是g(1)=6
最大值是g(9)=22