given that f(x)=x²-1 and g(x)=2x-3, the domain of (fοg)(x) will be as follows:
(fοg)(x) =(2x-3)^2-1
=4x²-12x+9-1
=4x²-12x+8
this is a quadratic function which has a positive coefficient of the highest power. Therefore the domain will be all real numbers.
