19.解:(1)3f(x)-f(2-x)=4x,①用2-x代替上式中的x,得3f(2-x)-f(x)=8-4x,②联立①②,可得∫(x)=x+1.(4分)设g(x)=ax2+bx+c,所以g(x+2)-g(x)=a(x+2)2+b(x+2)+c-a.即4ax+4a+2b=4x4a=4,所以解得a=1,b=-24a+2b=0,又g(1)=-4,得c=-3,所以g(x)=x2-2x-3(7分)(2)令f(x)≥g(x),即x+1≥x2-2x-3,x2-3x-4≤0,解得-1≤x≤4所以当x∈[-1,4]时,f(x)≥g(x)(9分)若要求x∈[m,n]时,恒有f(x)≥g(x)成立,可得n-m≤4-(-1)=5,即n-m的最大值是5(12分)

书面表达One possible version:NOTICEA sports meeting will be held in the playground of our school from next Thursday to FridayAs you know, the pressure of study is very heavy now, especially for those senior 3. So the purpose of the sports meeting is to letevery student get relaxed, as a result of which we students can live happily and heal thilyEveryone is welcome to take part in it. Those who perform excellently at the sports meeting will get prizes. But don' t take theresults so serously because taking part is more important than the result. Good luck to everyone!

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