For what interval is the value of (f – g)(x) negative?
(infinity,-1)
(infinity, 2)
(0,3)
(2,infinity)

Complete question:

Refer the attached diagram

In reference to the attached figure, (-∞, 2) is the value where (f-g) (x) negative.

Step-by-step explanation:

From the attached figure, it shows that given data:

f (x) = x – 3

g (x) = - 0.5 x

To Find: At what interval the value of (f-g) (x) negative

So, first we need to calculate the (f-g) (x)

(f – g ) (x) = f (x) – g (x) = x-3 - (- 0.5 x)

⇒ (f - g) (x) =1.5 x - 3

Now we are supposed to find the interval for which (f-g) (x) is negative.

⇒ (f - g) (x) = x - 3+ 0.5 x = 1.5 x – 3 < 0

⇒ 1.5 x – 3 < 0

⇒ 1.5 x < 3

⇒

⇒ x < 2

Thus for (f - g) (x) negative x must be less than 2. Thereby, the interval is (-∞, 2). Function is negative when graph line lies below the x - axis.