Answer
$(f\circ g)(x)=x^{2}-3$
$(g\circ f)(x)=x^{2}-6x+9$
Work Step by Step
$f(x)=x-3;$ $g(x)=x^{2}$
$(f\circ g)(x)$
To find $(f\circ g)(x)$, substitute $x$ by $g(x)$ in $f(x)$ and simplify:
$(f\circ g)(x)=f(g(x))=x^{2}-3$
$(g\circ f)(x)$
To find $(g\circ f)(x)$, substitute $x$ by $f(x)$ in $g(x)$ and simplify:
$(g\circ f)(x)=g(f(x))=(x-3)^{2}=x^{2}-6x+9$
