z=x^2+(x+1)^2=2x^2+2x+1=2(x+1/2)^2+1/2
x∈[-1,3/2]
则当x=-1/2时,z最小,为1/2
当x=3/2时,z最大,为17/2
所以z的值域为[1/2,17/2]