We can write the domain and range in interval notation, which uses values within brackets to describe a set of numbers. In interval notation, we use a square bracket [ when the set includes the endpoint and a parenthesis ( to indicate that the endpoint is either not included or the interval is unbounded.
If x - 4 ≥ 0, then |x - 4| = x - 4, so
G(x) = F(x) ⇒ 3x + 2 = (x - 4) + 2
⇒ 3x + 2 = x - 2
⇒ 2x = -4
⇒ x = -2
Otherwise, if x - 4 < 0, then |x - 4| = -(x - 4), so
G(x) = F(x) ⇒ 3x + 2 = -(x - 4) + 2
⇒ 3x + 2 = -x + 6
⇒ 4x = 4
⇒ x = 1
However,
• when x = -2, we have
G(-2) = 3(-2) + 2 = -4
F(-2) = |-2 - 4| + 2 = 8
• when x = 1, we have
G(1) = 3(1) + 2 = 5
F(1) = |1 - 4| + 2 = 5
so only x = 1 is a solution to G(x) = F(x).
Answer:
A
Step-by-step explanation:
28 + 8 is 26
