For what interval is the value of (f-g)(x) negative?

(-∞,2)

Step-by-step explanation:

Given : f(x)=x-3

           g(x)= - 0.5x

To Find : For what interval is the value of (f-g)(x) negative?

Solution :

First calculate the (f-g)(x)

Since  f(x)=x-3

           g(x)= - 0.5x

So, (f-g)(x) = x-3-(- 0.5x)

⇒(f-g)(x) = x-3+ 0.5x

⇒(f-g)(x) =1.5x-3

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

So, (f-g)(x) =1.5x-3 <0

⇒1.5x<3

⇒

⇒

Thus for (f-g)(x) negative x must be less than 2

Thus the interval is(-∞,2)

Hence option B is correct