Question

已知f(x)=2+log3(x),x∈[1,3]求y=[f(x)]^2+f(x^2)的值域

Answer 1

y=[f(x)]^2+f(x^2)

=(2+log3(x))+2+2log3(x)

=[log3(x)]^2+6log3(x)+6

令t=log3(x）

∵x∈[1,3] ∴t∈[0,1]

∴y=t^2+6t+6=(t+3)^2-3

∴该函数的值域为[6,13]