Answer
(a) $f(5)-g(5)=-101$
(b) $f(g(2))=f(18)=-1173$
(c) $f(3)g(3) =-414$
Work Step by Step
$f(x)=-4x^2+7x-3$
$g(x)=5x+8$
(a)
$f(5)-g(5)=-4(5)^2+7(5)-3-(5\times5+8)$
$f(5)-g(5)=-100+35-3-(25+8)$
$f(5)-g(5)=-68-33=-101$
(b)
$f(g(2))=f(5\times2+8)=f(18)$
$f(g(2))=f(18)=-4(18)^2+7(18)-3=-1296+126-3=-1173$
(c)
$f(3)g(3)$
$=[-4(3^2)+7\times3-3] [5\times3+8]$
$=[-4\times9+21-3] [15+8]$
$=[-36+21-3] [15+8]$
$=[-18] [23]$
$ =-414$
