Answer
a) $f(x) + g(x)= 1.5x + 9.5$
b) $f(g(x))= -7x + 23.25$
c) $f(x)g(x)= -7x^{2} + 11.25x + 22$
Work Step by Step
$f(x) = 3.5x + 4$
$g(x) = -2x + 5.5$
a) $f(x) + g(x)$
$= (3.5x + 4) + (-2x + 5.5)$
$= 3.5x - 2x + 4 + 5.5$
$= 1.5x + 9.5$
b) $f(g(x))$
$= f(-2x+5.5)$
$= 3.5(-2x+5.5) + 4$
$= -7x + 19.25 + 4$
$= -7x + 23.25$
c) $f(x)g(x)$
$= (3.5x+4)(-2x+5.5)$
$= 3.5x(-2x+5.5) + 4(-2x+5.5)$
$= -7x^{2} + 19.25x -8x + 22$
$= -7x^{2} + 11.25x + 22$
