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