Answer
$a)$ $(f\circ f)(x)=4x-9$
$b)$ $(g\circ g)(x)=-x^{4}+8x^{2}-12$
Work Step by Step
$f(x)=2x-3,$ $g(x)=4-x^{2}$
$a)$ $(f\circ f)(x)$
Substitute $f(x)$ into itself and simplify:
$(f\circ f)(x)=f(f(x))=2(2x-3)-3=4x-6-3=4x-9$
$b)$ $(g\circ g)(x)$
Substitute $g(x)$ into itself and simplify:
$(g\circ g)(x)=g(g(x))=4-(4-x^{2})^{2}=4-(16-8x^{2}+x^{4})=...$
$...=4-16+8x^{2}-x^{4}=-x^{4}+8x^{2}-12$
