# f(x)=x−3 and g(x)=4x2−3x−9g(x)=4x^2−3x−9. Find composite function f∘g and g∘f

Composite functions

f(x)=x−3 and $$\displaystyle{g{{\left({x}\right)}}}={4}{x}{2}−{3}{x}−{9}{g{{\left({x}\right)}}}={4}{x}^{{2}}−{3}{x}−{9}$$. Find composite function $$\displaystyle{f}∘{g}$$ and $$\displaystyle{g}∘{f}$$

We are given: f(x)=x-3 and g(x) = $$\displaystyle{4}{x}^{{2}}-{3}{x}-{9}$$
$$(f ∘ g)(x)=f(g(x)) =(4x^2-3x-9)-3 =4x^2-3x-12$$
$$(g ∘ f)(x)=g(f(x)) =4((x-3)^2)-3(x-3)-9 =4(x^2-6x+9)-3(x-3)-9 =4x^2-24x+36-3x+9-9 =4x^2-27x+36$$