Question

The graphs of f (x) and g (x) are shown below.

Answer 1

B) (-∞, 2)

Explanation:

Given functions:

`f(x)=x-3`

`g(x)=-0.5x`

To find the interval for which (f - g)(x) is negative, set (f - g)(x) less than zero and solve for x:

`\begin{aligned}(f-g)(x)& < 0\\f(x)-g(x)& < 0\\(x-3)-(-0.5x)& < 0\\x-3+0.5x& < 0\\1.5x-3& < 0\\1.5x& < 3\\x& < 2\end{aligned}`

Therefore, the interval for which the composite function (f - g)(x) is negative is:

• (-∞, 2)