Answer
$a)$ $f(f(2))=-1$
$b)$ $g(g(3))=-21$
Work Step by Step
$f(x)=2x-3;$ $g(x)=4-x^{2}$
$a)$ $f(f(2))$
Find $f(2)$ by substituting $x$ with $2$ in $f(x)$:
$f(2)=2(2)-3=4-3=1$
Substitute $x$ with $1$, also in $f(x)$:
$f(f(2))=f(1)=2(1)-3=2-3=-1$
$b)$ $g(g(3))$
Find $g(3)$ by substituting $x$ with $3$ in $g(x)$:
$g(3)=4-(3)^{2}=4-9=-5$
Substitute $x$ with $-5$, also in $g(x)$:
$g(g(3))=g(-5)=4-(-5)^{2}=4-25=-21$
