We are given: f(x)=x-3 and g(x) = \(\displaystyle{4}{x}^{{2}}-{3}{x}-{9}\)

To find f o g replace x of x by g(x) and simplify:

\((f ∘ g)(x)=f(g(x)) =(4x^2-3x-9)-3 =4x^2-3x-12\)

To find g o f, replace x of g by f(x) and simplify:

\((g ∘ f)(x)=g(f(x)) =4((x-3)^2)-3(x-3)-9 =4(x^2-6x+9)-3(x-3)-9 =4x^2-24x+36-3x+9-9 =4x^2-27x+36\)