fx=sin(πx/3-π/6)-2cos^2(πx/6)
=sin(πx/3)×√3/2-cos(πx/3)×1/2-cos(πx/3)-1
= √3/2×sin(πx/3)-3/2×cos(πx/3)-1
=√3sin(πx/3-π/3)-1
最小正周期T=2π/(π/3)=6
2Kπ-π/2≤πx/3-π/3≤2Kπ+π/2,k∈Z
6K-1/2≤x≤6K+5/2,k∈Z
函數(shù)的單調(diào)遞增區(qū)間
[6K-1/2,6K+5/2],k∈Z
單調(diào)遞減區(qū)間
[6K+5/2,6K+11/2],k∈Z
2
∵y=gx與y=fx的圖像關(guān)于直線x=2對稱
∴g(x)=√3sin[π/3(4-x)-π/3]-1
=√3sin[4π/3 -πx/3 -π/3]-1
=√3sin[π -πx/3 ]-1
=√3sin(πx/3)-1
∵0≤x≤1∴ 0≤πx/3≤π/3
∴0≤sin(πx/3)≤√3/2
∴-1≤g(x)≤1/2
∴x=1時,g(x)取得最大值1/2