Question

已知函数f(x)=3+log2(为底)x,x∈[1,16],g(x)=2f(x^2)+[f(x)]^2,

Answer 1

g(x)=2f(x^2)+[f(x)]^2,则x^2∈[1,16],且x∈[1,16],即g(x)的定义域为x∈[1,4]

g(x)=2f(x^2)+[f(x)]^2=2(3+2log2X)+9+(log2X)^2+6log2X,

令y=log2X,y∈[0,2],g(x)=y^2+10y+15,易知其在y∈[0,2]上为单调增函数,g(x)值域为[15,39]