Question

F(x)=x-3g(x)=-0.5xfor what interval is the value of (f-g)(x) negative?

Answer 1

Given the functions:

`\begin{gathered} f(x)=x-3 \\ g(x)=-0.5x \end{gathered}`

1. You need to subtract the function g(x) from the function f(x), in order to find:

`(f-g)(x)`

Then, you get:

`(f-g)(x)=x-3-(-0.5x)`
`(f-g)(x)=x-3+0.5x`
`(f-g)(x)=1.5x-3`

2. By definition, negative numbers are less than zero. Therefore, you can set up the following inequality:

`1.5x-3<0`

3. Solve for "x":

`1.5x<3`
`x<(3)/(1.5)`
`x<2`

4. Write the solution in Interval Notation, in order to determine the interval for which the value of the function obtained by subtracting the given functions is negative (as the symbol of the inequality is "Less than", 2 is not included. Then, you must use parentheses):

`(-\infty,2)`

Hence, the answer is:

`(-\infty,2)`