(1)把函数F(X)的图像上每一点的横坐标缩短为原来的1/2是g(x)=2COS2X
纵坐标不变,然后再向右平移π/6个单位后为g(x)=2COS(2X-π/3)
∴g(x)=2COS(2X-π/3)
(2)y=2COS(2X-π/3)+4COS²X
=cos2x+√3sin2x+2cos2x+2
=√3sin2x+3cos2x+2
=√3(sin2x+√3cos2x)+2
=2√3sin(2x+л/3)+2
∵0≤x≤л/3
∴0≤2x≤2л/3
∴л/3≤2x+л/3≤л
∴0≤sin(2x+л/3)≤√3/2
∴2≤y≤5
∴y在[0,π/3]上的值域为[2,5]