f(x)=sin²x+sinxcosx
=(1-cos2x)/2+(1/2)sin2x
=(1/2)(sin2x-cos2x)+1/2
=(√2/2)[sin2xcosπ/4-cos2xsinπ/4)+1/2
=(√2/2)sin(2x-π/4)+1/2
因为:-3π/8≤x≤π/4
-3/4π≤2x≤π/2
-π≤2x-π/4≤π/4
所以：sin(2x-π/4)的最小值为-1；最大值为√2/2
所以：
f(x)的最大值=(√2/2)²+1/2=1
最小值=-√2/2+1/2=(1-√2)/2
值域为：【(1-√2)/2 ,1】