Answer
$(f\circ g)(x)=-8x^{3}-2x-2$
$(g\circ f)(x)=-2x^{3}-2x+4$
Work Step by Step
$f(x)=x^{3}+x-2;$ $g(x)=-2x$
$(f\circ g)(x)$
To find $(f\circ g)(x)$, substitute $x$ by $g(x)$ in $f(x)$ and simplify:
$(f\circ g)(x)=f(g(x))=(-2x)^{3}-2x-2=...$
$...=-8x^{3}-2x-2$
$(g\circ f)(x)$
To find $(g\circ f)(x)$, substitute $x$ by $f(x)$ in $g(x)$ and simplify:
$(g\circ f)(x)=g(f(x))=-2(x^{3}+x-2)=-2x^{3}-2x+4$
