Question

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

Answer 1

Answer: SECOND OPTION.

Step-by-step explanation:

1. You must subtract the function f(x) and g(x), therefore, you obtain:

$(f-g)(x)=x-3-(-0.5x)\\(f-g)(x)=x-3+0.5x\\(f-g)(x)=1.5x-3$

2. When you graph$(f-g)(x)=1.5x-3$, you obtain the graph shown attached.

3. As you can see, the interval in which the value $(f-g)(x)$ is negative is:

(-∞,2)

Therefore the answer is the second option.

Answer 2

Answer:

The correct option is 2.

Step-by-step explanation:

From the given graphs in is clear that

$f(x)=x-3$

$g(x)=-0.5x$

we need to find the interval for which (f-g)(x) is negative.

$(f-g)(x)=f(x)-g(x)$

Substitute the values of both functions.

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

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

$(f-g)(x)=1.5x-3$

The value of (f-g)(x) is negative mean the value (f-g)(x) is less than 0.

$1.5x-3<0$

Add 3 on both sides.

$1.5x<3$

Divide both sides by 1.5.

$\frac{1.5x}{1.5}<\frac{3}{1.5}$

$x<2$

For all x<2, the value (f-g)(x) is negative. It means for the interval (-∞,2) the value (f-g)(x) is negative.

Therefore the correct option is 2.