m+n=(sinx+cosx,1/2)
(m+n)*m=sinx(sinx+cosx)-1/2
=sinxcosx+sin²x-1/2
=(1/2)sin2x+(1-cos2x)/2-1/2
=(1/2)sin2x-(1/2)cos2x
=(√2/2)sin(2x-π/4)
所以,f(x)=(√2/2)sin(2x-π/4)
xx属于[0,π/2],则：2x-π/4属于[-π/4,3π/4]
所以,sin(2x-π/4)属于[-√2/2,√2/2]
所以,(√2/2)sin(2x-π/4)属于[-1,1]
即f(x)的值域为[-1,1]
祝你开心!希望能帮到你,如果不懂,请追问,祝学习进步!O(∩_∩)O