g(x)定义域
1≤x≤4 1≤x^2≤4
解得1≤x≤2
g(x)=-[f(x)]^2+f(x^2)
=-(3+log(2)x)^2+3+log(2)x^2
=-(3+log(2)x)^2+3+2log(2)x
令log(2)x=t 1≤x≤2
则0≤t=log(2)x≤1
=-(3+t)^2+3+2t
=-t^2-4t-6
=-(t+2)^2-2
对称轴t=-2
则在t∈[0,1]上单调递减
t=0即x=1时 最大值g(1)=-6
t=1即x=2时 最小值g(2)=-11
g(x)定义域
1≤x≤4 1≤x^2≤4
解得1≤x≤2
g(x)=-[f(x)]^2+f(x^2)
=-(3+log(2)x)^2+3+log(2)x^2
=-(3+log(2)x)^2+3+2log(2)x
令log(2)x=t 1≤x≤2
则0≤t=log(2)x≤1
=-(3+t)^2+3+2t
=-t^2-4t-6
=-(t+2)^2-2
对称轴t=-2
则在t∈[0,1]上单调递减
t=0即x=1时 最大值g(1)=-6
t=1即x=2时 最小值g(2)=-11