Question

Let g be the piecewise defined function shown.g(x)= x + 4, −5 ≤ x ≤ −12 − x, −1 < x ≤ 5Evaluate g at different values in its domain.I don't understand why g(0)=2 because 0 can fit into both domain values.ex. -5 ≤ 0 ≤ 1 -1 < 0 ≤ 5

Answer 1

Given:

[tex]g(x)=\left\{ \begin{aligned}x+4,-5\le x\le-1 \\ 2-x,-1For the domain values, we have:

For −5 ≤ x ≤ −1

Lets take all range of values of x

g(-5) = x + 4 = -5 + 4 = -1

g(-4) = x + 4 = -4 + 4 = 0

g(-3) = x + 4 = -3 + 4 = 1

g(-2) = x + 4 = -2 + 4 = 2

g(-1) = x + 4 = -1 + 4 = 3

For −1 < x ≤ 5

Lets take all range of values of x

g(0) = 2 - x = 2 - 0 = 2

g(1) = 2 - x= 2 - 1 = 1

g(2) = 2 - x= 2 - 2 = 0

g(3) = 2 - x= 2 - 3 = -1

g(4) = 2 - x= 2 - 4 = -2

g(5) = 2 - x= 2 - 5 = -3