Question

已知向量a=(2根号3 sinx,cos^x),b=(cosx,2)函数f(x)=a*b

Answer 1

f(x)=a*b=2根号3sinxcosx+2cos^2x=根号3sin2x+cos2x+1=2sin(2x+Pai/6)+1

单调减区间是:2kPai+Pai/2<=2x+Pai/6<=2kPai+3Pai/2
即有[kPai+Pai/6,kPai+2Pai/3]
(2)f(x)向左平移Pai/12后是f(x)=2sin(2(x+Pai/12)+Pai/6),再把各个横坐标缩短为原来的1/2后得到g(x)=2sin(4x+Pai/3)
0<=x<=Pai/4
Pai/3<=4x+Pai/3<=4Pai/3
-根号3/2<=sin(4x+Pai/3)<=1
故值域是[-根号3,2]