If g(x) = x2 + 3x + 4, find g(x + 1) – g(x)
-
A.
(x + 2) -
B.
2(x + 2) -
C.
(2x + 1) -
D.
(x2 + 4)
Correct Answer: Option B
Explanation
g(x) = x2 + 3x + 4
= g(x + 1) = (x + 1)^2 + 3(x + 1) + 4
= x2 + 1 + 2x + 3x + 3 + 4
= x2 + 5x + 8
g(x + 1) – g(x) = x2 + 5x + 8 – (x2 + 3x + 4)
= x2 + 5x + 8 – x2 + 3x + 4
= 2x + 4
= 2(x + 2)