The (f-g)(x) is negative in the interval (-∞, 2). Therefore, option B is the correct option.
We need to find for what interval is the value of (f-g)(x) negative.
How do you find intervals of a function?
To find the increasing intervals of a given function, one must determine the intervals where the function has a positive first derivative.
Now, we are given a straight line with a positive slope f(x)=x-3.
The line passes through (0,-3) and (3,0).
g(x)=-0.5x
The line goes through (-4,2),(0,0) and (4,-2).
We have to find in which interval the value of (f-g)(x) is negative.
(f-g)(x)=x-3+0.5x=1.5x-3
When x is negative than (f-g)(x) is negative when x is positive except at x=2 then (f-g)(x) is positive.
When x is 2 the (f-g)(x)=0.
When x is 0 then (f-g)(x) is negative.
Therefore, option B is the correct option.
To learn more about the intervals of function visit:
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