Answer
$a)$ $(f\circ g)(-2)=-3$
$b)$ $(g\circ f)(-2)=-45$
Work Step by Step
$f(x)=2x-3;$ $g(x)=4-x^{2}$
$a)$ $(f\circ g)(-2)$
Find $g(-2)$ by substituting $x$ with $-2$ in $g(x)$:
$g(-2)=4-(-2)^{2}=4-4=0$
Substitute $x$ with $0$ in $f(x)$:
$(f\circ g)(-2)=f(0)=2(0)-3=-3$
$b)$ $(g\circ f)(-2)$
Find $f(-2)$ by substituting $x$ with $-2$ in $f(x)$:
$f(-2)=2(-2)-3=-4-3=-7$
Substitute $x$ with $-7$ in $g(x)$:
$(g\circ f)(-2)=g(-7)=4-(-7)^{2}=4-49=-45$
