Identify the domain and range.

y = –1.5x²

since y = –1.5x² its domain is  R=] -infinity,  infinity[
the inverse of y
–1/1.5 y = x² , and x = sqrt ((–1/1.5) y) , and f^-1 (x) = sqrt ((–1/1.5) x)
its domain is –1/1.5) x>=0, so x<=0, 
from where, the range of y = –1.5x² is the interval ]-infinity, 0]