9 12 pts Let f x 4x2 2x 8 and gx 1 2x a Evaluate the fu

9. (12 pts) Let f (x) = 4x² + 2x – 8 and g(x) = 1 – 2x.

(a) Evaluate the function g – f for x = –3. That is, find (g – f)(–3). Show work.

(b) Evaluate the function fg for x = –3. That is, find (f g)( –3). Show work.

(c) Find the difference function (f – g)(x) and simplify the results. Show work.

Solution

f(x) = 4x² + 2x – 8 and g(x) = 1 – 2x

a) (g - f) = g(x) - f(x)

==> g - f = 1 – 2x - (4x² + 2x – 8)

==> g - f = 1 - 2x -4x² -2x +8 = -4x² -4x + 9

==> (g - f)(-3) = -4(-3)² -4(-3) + 9 = -36 + 12 + 9

==> (g - f)(-3) = -15

b) fg = f(x) g(x)

==> fg = (4x² + 2x – 8) (1 – 2x)

==> fg = 4x² -8x³ + 2x -4x² -8 + 16x

==> fg = -8x³ + 18x -8

==> (fg)(-3) = -8(-3)³ + 18(-3) -8

==> (fg)(-3) = 216 -54 -8 = 154

c) (f - g)(x) = f(x) - g(x)

==> (f - g)(x) = (4x² + 2x – 8) - (1 -2x)

==> (f - g)(x) =4x² + 2x – 8 - 1 +2x

==> (f - g)(x) = 4x² + 4x – 9