Determine the composition of the functions $f(x)=4x+3$ and $g(x)=-5x^2+1$

Question

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?

Answer 1

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:

$$-5(16x^2+24x+9)+1=-80x^2-120x-45+1$$ $$=-80x^2-120x-44$$