Concept:Function substitution and simplification of a difference expression.Explanation:Start with g(x)=x2+3x.To find g(x+1), replace every x in g(x) with (x+1).So, g(x+1)=(x+1)2+3(x+1).Expand (x+1)2 as x2+2x+1.Then g(x+1)=x2+2x+1+3x+3.Simplify: g(x+1)=x2+5x+4.Now compute g(x+1)−g(x).g(x+1)−g(x)=(x2+5x+4)−(x2+3x).Remove brackets: x2+5x+4−x2−3x.The x2 terms cancel, leaving 2x+4.Factorise: 2x+4=2(x+2).Answer:g(x+1)−g(x)=2(x+2).Therefore, the correct option is B. 2(x + 2).