Answer
(a) $f(g(x))=-3.84x-15.4$
(b) $f(x)g(x)=-3.84x^2-11.68x+55.8$
(c) $g(3)-f(3)=14.8$
Work Step by Step
$f(x)=-2.4x+6.2$
$g(x)=1.6x+9$
(a) Determine $f(g(x))$:
$=f(1.6x+9)$
$=-2.4(1.6x+9)+6.2$
$=-2.4\times1.6x-2.4\times9+6.2$
$=-3.84x-21.6+6.2$
$=-3.84x-15.4$
(b) Determine $f(x)g(x))$:
$f(x)g(x)=(-2.4x+6.2)(1.6x+9)$
$=-2.4x(1.6x+9)+6.2(1.6x+9)$
$=-2.4\times1.6x^2-2.4\times9x+6.2\times1.6x+6.2\times9$
$=-3.84x^2-21.6x+9.92x+55.8$
$=-3.84x^2-11.68x+55.8$
(c) Determine $g(3)-f(3)$:
$g(3)-f(3)=1.6\times3+9-(-2.4\times3+6.2)$
$=4.8+9-(-7.2+6.2)$
$=13.8+7.2-6.2$
$=14.8$
