Answer
(a) $f(g(x))=5.25x+18$
(b) $g(f(6))=56.25$
(c) $g(x)-f(x)=2x+4.5$
Work Step by Step
$f(x)=1.5x+4.5$
$g(x)=3.5x+9$
(a) Determine $f(g(x))$:
$f(g(x))=f(3.5x+9)$
$=2.5(3.5x+9)+4.5$
$=5.25x+13.5+4.5$
$=5.25x+18$
(b) Determine $g(f(x))$:
$g(f(x))=g(1.5x+4.5)$
$= 3.5(1.5x+4.5)+9$
$=5.25x+15.75+9$
$=5.25x+24.75$
$g(f(x))=5.25x+24.75$
Put $x=6$ in $g(f(x))$:
$g(f(6))=5.25(6)+24.75=56.25$
(c) Determine $g(x)-f(x)$:
$g(x)-f(x)=(3.5x+9)-(1.5x+4.5)$
$=3.5x+9-1.5x-4.5$
$=2x+4.5$