Answer
$a)$ $(f\circ g)(x)=-2x^{2}+5$
$b)$ $(g\circ f)(x)=-4x^{2}+12x-5$
Work Step by Step
$f(x)=2x-3,$ $g(x)=4-x^{2}$
$a)$ $(f\circ g)(x)$
Substitute $g(x)$ into $f(x)$ and simplify the function:
$(f\circ g)(x)=f(g(x))=2(4-x^{2})-3=8-2x^{2}-3=-2x^{2}+5$
$b)$ $(g\circ f)(x)$
Substitute $f(x)$ into $g(x)$ and simplify the function:
$(g\circ f)(x)=g(f(x))=4-(2x-3)^{2}=4-(4x^{2}-12x+9)=...$
$...=4-4x^{2}+12x-9=-4x^{2}+12x-5$
