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]