The interval is the value (-∞,2)
We have given that,
f(x)=x-3
g(x)= - 0.5x
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
[tex]x < \frac{3}{1.5} \\x < 2[/tex]
Thus for (f-g)(x), negative x must be less than 2
Thus the interval is(-∞,2)
Hence option B is correct.
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