Answer
$a.\quad f\circ g$
$b.\quad j\circ g$
$c.\quad g\circ g$
$d.\quad j\circ j$
$e.\quad g\circ h\circ f$
$f.\quad h\circ j\circ f$
Work Step by Step
$f(x)=x-3$
$g(x)=\sqrt{x}$
$h(x)=x^3$
$j(x)=2x$
$a.\quad f(g(x))=f(\sqrt{x})=\sqrt{x}-3$
$b.\quad j(g(x))=j(\sqrt{x})=2\sqrt{x}$
$c.\quad g(g(x))=g(x^{\frac{1}{2}})$
$=(x^{\frac{1}{2}})^{\frac{1}{2}}=x^{\frac{1}{4}}$
$d.\quad j(j(x))=j(2x)=2(2x)=4x$
$e.\quad g(h(f(x)))=g(h(x-3))=g((x-3)^3)$
$=\sqrt{(x-3)^3}$
$f.\quad h(j(f(x)))=h(j(x-3))=h(2x-6)$
$=(2x-6)^3$
