Question

已知f(x)=2+log3x,x∈[1,3],求函数y=[f(x)]^2+f(x^2)的值域

Answer 1

y=(2+log3x)^2+2+log3(x^2)

=(log3x)^2+4log3x+4+2log3x+2

=(log3x)^2+6log3x+6

=(3+log3x)^2-3

x∈[1,3]

log3x∈[0,1]

3+log3x∈[3,4]

(3+log3x)^2∈[9,16]

y=(3+log3x)^2-3∈[6,13]