Answer
$(f\circ g)(x)=-4x^{3}-4x^{2}+24$
$(g\circ f)(x)=-64x^{3}+16x^{2}-6$
Work Step by Step
$f(x)=-4x$ $;$ $g(x)=x^{3}+x^{2}-6$
$(f\circ g)(x)$
To find $(f\circ g)(x)$, substitute $x$ by $g(x)$ in $f(x)$ and simplify:
$(f\circ g)(x)=f(g(x))=-4(x^{3}+x^{2}-6)=-4x^{3}-4x^{2}+24$
$(g\circ f)(x)$
To find $(g\circ f)(x)$, substitute $x$ by $f(x)$ in $g(x)$ and simplify:
$(g\circ f)(x)=g(f(x))=(-4x)^{3}+(-4x)^{2}-6=...$
$...=-64x^{3}+16x^{2}-6$
