已知函数f(x)=-√3sin²x+sinxcosx

f(x)=-√3sin²x+sinxcosx=-√3(1-cos2x)/2+sin2x/2=-√3/2+√3/2cos2x+sin2x/2=-√3/2+sin(2x+π/3)∵x∈[0,π/2]∴2x+π/3∈[π/3,4π/3]∴sin(2x+π/3)∈[-√3/2,1]∴值域为[-√3,(2-√3)/2]您好,很高兴为您...