Answer
$a)$ $f(g(0))=5$
$b)$ $g(f(0))=-5$
Work Step by Step
$f(x)=2x-3;$ $g(x)=4-x^{2}$
$a)$ $f(g(0))$
Find $g(0)$ by substituting $x$ with $0$ in $g(x)$:
$g(0)=4-(0)^{2}=4$
Substitute $x$ with $4$ in $f(x)$:
$f(g(0))=f(4)=2(4)-3=8-3=5$
$b)$ $g(f(0))$
Find $f(0)$ by substituting $x$ with $0$ in $f(x)$:
$f(0)=2(0)-3=-3$
Substitute $x$ with $-3$ in $g(x)$
$g(f(0))=g(-3)=4-(-3)^{2}=4-9=-5$
