已知定义域为[0,1]的函数f(x)同时满足以下三个条件:
1个回答

(1)取x 1=x 2=0,代入f(x 1+x 2)≥f(x 1)+f(x 2),

得f(0)≥f(0)+f(0),化简可得f(0)≤0

又由f(0)≥0,得f(0)=0

(2)显然g(x)=2 x-1在[0,1]上满足[Ⅰ]g(x)≥0;[Ⅱ]g(1)=1.

若x 1≥0,x 2≥0,且x 1+x 2≤1,则有

g(x 1+x 2)-[g(x 1)+g(x 2)]= 2 x 1 + x 2 -1-[( 2 x 1 -1)+( 2 x 2 -1)]=( 2 x 2 -1)( 2 x 1 -1)≥0

故g(x)=2 x-1满足条件[1]、[2]、[3],所以g(x)=2 x-1为友谊函数.