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JAMB 1991 · UME · Q16

If g(x)=x2+3xg(x) = x^2 + 3x, find g(x+1)−g(x)g(x + 1) - g(x).

Worked solution (try it first)
  1. g(x+1)=(x+1)2+3(x+1)g(x + 1) = (x + 1)^2 + 3(x + 1)
    =x2+2x+1+3x+3= x^2 + 2x + 1 + 3x + 3.
  2. Subtract g(x)=x2+3xg(x) = x^2 + 3x: the x2x^2 and 3x3x cancel, leaving 2x+42x + 4.
  3. So g(x+1)−g(x)=2(x+2)g(x + 1) - g(x) = 2(x + 2), option B.

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