已知函数f(x)=[cos(x+π/12)]^2,g(x)=1+1/2sin2x.求:

问题描述:

已知函数f(x)=[cos(x+π/12)]^2,g(x)=1+1/2sin2x.求:
(1)设x=x0是函数y=f(x)图像的一条对称轴,求g(2x0)的值; (2)求函数h(x)=f(x)+g(x),x∈[0,π/4]的值域.

f(x)=[cos(x+π/12)]^2=[1+cos{2(2x+π/6)}]÷2 (x=5π/12对称轴) 代入g(x)=1+1/2sin2x=5/4 (2)h(x)=[cos(x+π/12)]^2+1+1/2sin2x=3/2+1/4sin2x+√3/4cos2x=2/3+1/2sin(π/3+2x) 至于值域自己会球吧...