For what interval is the value of (f – g)(x) negative, where f(x) = (x - 3) and g(x) = -0.5x?

Functions are the basis of many mathematical concepts like calculus and algebra. All the fundamental operations like addition and subtraction can be performed on functions.

Answer: The value of (f – g)(x) is negative in the interval (-∞, 2).

Let's understand the solution in detail.

Explanation:

We have:

f(x) = x - 3

g(x) = -0.5x

Now:

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

= x + 0.5x - 3 

= 1.5x - 3

Now, we have to find the region where (f - g) (x) is negative.

Hence, 1.5x - 3 < 0

Now, from the above inequality, we get x < 2.

Hence, the value of (f – g)(x) negative is negative in the interval (-∞, 2).