If g(x) = x2 + 3x + 4, find g(x + 1) - g(x)
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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)
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)