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If g x x2 3x 4 find g x 1 - g x - JAMB Mathematics 1991 Question

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)
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Correct Option: B

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)

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