求函数F(x)=根号3乘sinx+cosx+3

f(x)=√3sinx+cosx+3
=2[(√3/2)sinx+(1/2)cosx]+3
=2sin(x+π/6) +3
当sin(x+π/6)=1时,f(x)有最大值[f(x)]max=2+3=5
当sin(x+π/6)=-1时,f(x)有最小值[f(x)]min=-2+3=1
函数的值域为[1,5].