<s>[INST] Determine the composition of the functions $f(x)=4x+3$ and $g(x)=-5x^2+1$ Answer: 
\begin{align*}
(f \circ g)(x) & = f(g(x))\\
               & = 4(-5x^2+1)+3\\
               & = -20x^2+8+3\\
               & = -20x^2+11
\end{align*}
\begin{align*}         
(g \circ f)(x) & = g(f(x))\\
               & = -5(4x+3)^2+1\\
               & = -5[(4x+3)(4x+3)]+1\\
               & = -5(16x^2+24x+9)+1\\
               & = -80x^2-19x-45+1\\
               & = -80x^2-19x-44
\end{align*}
Is my working out and answer correct?
 [/INST] You have the right idea, except your algebra is off. For the first one 
$$4(-5x^2+1)+3=-20x^2+4+3$$
$$=-20x^2+7$$
For the second one:
$$-5(16x^2+24x+9)+1=-80x^2-120x-45+1$$
$$=-80x^2-120x-44$$
</s>