Question

Find a number x such that g(x) = -4

Answer 1

C: x = 7

Explanation:

The easiest way to do this is to simply try all of the x-vales given as options.

Option 1: x = -1

Since
`-1 \leq 0`, we'll use the first equation.

`g(x)=\mid x \mid - 2\\g(-1)=\mid -1 \mid - 2 = 1 - 2 = -1`

As we can see, g(-1) is not -4.

Option 2: x = 3

Since
`0 < 3 < 4`, we'll use the 2nd equation.

`g(x) = x-3\\g(3) = 3-3 = 0`

Not -4.

Option 3: x = 7

Since
`4 \leq 7`, we'll use the 3rd equation.

`g(x) = 3-x\\g(7) = 3-7 = -4`

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
`4 \leq 4` (less than or equal to), we'll use the 3rd equation.

`g(x) = 3-x\\g(4) = 3-4 = -1`