find the domain and range of function

f(x) = 3 / 2 - x ²

For domain: 2 - x²  should not equal zero, i.e 2 shold not equal x ²

^{Domain { x : x} R< x sq root 2}

For range

2y - x²y=3

x²= (2y-3)/y

x = Sq root  (2y-3)/y

For (2y-3)/y to be positive either both Nr and Dr should be positive , in which case y>3/2 . Or else both should be negative , in which case y <0.

Range  is therefore all  real numbers except between 0 and 3/2 , both included