Answer:
C: x = 7
Step-by-step explanation:
The easiest way to do this is to simply try all of the x-vales given as options.
Option 1: x = -1
Since [tex]-1 \leq 0[/tex], we'll use the first equation.
[tex]g(x)=\mid x \mid - 2\\g(-1)=\mid -1 \mid - 2 = 1 - 2 = -1[/tex]
As we can see, g(-1) is not -4.
Option 2: x = 3
Since [tex]0 < 3 < 4[/tex], we'll use the 2nd equation.
[tex]g(x) = x-3\\g(3) = 3-3 = 0[/tex]
Not -4.
Option 3: x = 7
Since [tex]4 \leq 7[/tex], we'll use the 3rd equation.
[tex]g(x) = 3-x\\g(7) = 3-7 = -4[/tex]
Tada! We have found a number such that g(x) = -4, it is 7. Since we only need to find a number, not all numbers, we don't have to check the last option. However, if you're curious:
Option 4: x = 4
Since [tex]4 \leq 4[/tex] (less than or equal to), we'll use the 3rd equation.
[tex]g(x) = 3-x\\g(4) = 3-4 = -1[/tex]
