Answer
$a)$ $(f\circ f)(-1)=-13$
$b)$ $(g\circ g)(-1)=-5$
Work Step by Step
$f(x)=2x-3;$ $g(x)=4-x^{2}$
$a)$ $(f\circ f)(-1)$
Find $f(-1)$ by substituting $x$ with $-1$ in $f(x)$:
$f(-1)=2(-1)-3=-2-3=-5$
Substitute $x$ with $-5$, also in $f(x)$:
$(f\circ f)(-1)=f(-5)=2(-5)-3=-10-3=-13$
$b)$ $(g\circ g)(-1)$
Find $g(-1)$ by substituting $x$ with $-1$ in $g(x)$:
$g(-1)=4-(-1)^{2}=4-1=3$
Substitute $x$ with $3$, also in $g(x)$:
$(g\circ g)(-1)=g(3)=4-(3)^{2}=4-9=-5$
