Answer :
[tex]g \circ f=-(2x-3)^2-1=-(4x^2-12x+9)-1=\\
=-4x^2+12x-9-1=-4x^2+12x-10\\[/tex]
[tex]f(x)=2x-3\ \ \ and\ \ \ g(x)= -x^2-1\\\\( g \circ f) (x)=g\bigg(f(x)\bigg)=g\bigg(2x-3\bigg)=-(2x-3)^2-1=\\\\=-(4x^2-12x+9)-1=-4x^2+12x-9-1=-4x^2+12x-10[/tex]