快,详解··21.已知定义域为[0,1]的函数f(x)同时满足①对于任意的x∈[0,1],总有f(x) ≥0,②f⑴=1③x1≥0,x2≥0,x1=x2≤1时有f(x1+x2)≥f(x1)+f(2)1.求f(0)的值,2.求函数f(x)的最大值3.证明当x∈
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![快,详解··21.已知定义域为[0,1]的函数f(x)同时满足①对于任意的x∈[0,1],总有f(x) ≥0,②f⑴=1③x1≥0,x2≥0,x1=x2≤1时有f(x1+x2)≥f(x1)+f(2)1.求f(0)的值,2.求函数f(x)的最大值3.证明当x∈](/uploads/image/z/3631547-11-7.jpg?t=%E5%BF%AB%2C%E8%AF%A6%E8%A7%A3%C2%B7%C2%B721.%E5%B7%B2%E7%9F%A5%E5%AE%9A%E4%B9%89%E5%9F%9F%E4%B8%BA%5B0%2C1%5D%E7%9A%84%E5%87%BD%E6%95%B0f%28x%29%E5%90%8C%E6%97%B6%E6%BB%A1%E8%B6%B3%E2%91%A0%E5%AF%B9%E4%BA%8E%E4%BB%BB%E6%84%8F%E7%9A%84x%E2%88%88%5B0%2C1%5D%2C%E6%80%BB%E6%9C%89f%28x%29+%E2%89%A50%2C%E2%91%A1f%E2%91%B4%3D1%E2%91%A2x1%E2%89%A50%2Cx2%E2%89%A50%2Cx1%3Dx2%E2%89%A41%E6%97%B6%E6%9C%89f%EF%BC%88x1%2Bx2%EF%BC%89%E2%89%A5f%EF%BC%88x1%EF%BC%89%2Bf%EF%BC%882%EF%BC%891.%E6%B1%82f%EF%BC%880%EF%BC%89%E7%9A%84%E5%80%BC%2C2.%E6%B1%82%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC3.%E8%AF%81%E6%98%8E%E5%BD%93x%E2%88%88)
快,详解··21.已知定义域为[0,1]的函数f(x)同时满足①对于任意的x∈[0,1],总有f(x) ≥0,②f⑴=1③x1≥0,x2≥0,x1=x2≤1时有f(x1+x2)≥f(x1)+f(2)1.求f(0)的值,2.求函数f(x)的最大值3.证明当x∈
快,详解··
21.已知定义域为[0,1]的函数f(x)同时满足①对于任意的x∈[0,1],总有f(x) ≥0,②f⑴=1③x1≥0,x2≥0,x1=x2≤1时有f(x1+x2)≥f(x1)+f(2)
1.求f(0)的值,
2.求函数f(x)的最大值
3.证明当x∈(1/2,1]时,f(x)<2x; 当x∈[0,1/2]时,f(x)≤1/2 f(2x)
必要详解··一定···过程··
快,详解··21.已知定义域为[0,1]的函数f(x)同时满足①对于任意的x∈[0,1],总有f(x) ≥0,②f⑴=1③x1≥0,x2≥0,x1=x2≤1时有f(x1+x2)≥f(x1)+f(2)1.求f(0)的值,2.求函数f(x)的最大值3.证明当x∈
1、由f(x1+x2)≥f(x1)+f(x2),令x1=x2=0得:f(0)≥2f(0),即f(0)≤0;
又根据题设:①对于任意的x∈[0,1],总有f(x) ≥0,∴f(0)=0;
2、由f(x1+x2)≥f(x1)+f(x2)得:f(x1+x2)-f(x2)≥f(x1),
设0≤X1≤X2≤1,令X2=x1+x2,X1=x2,x1=X2-X1≥0
∴f(X2)-f(X1)≥f(X2-X1)≥0,f(x) 为增函数,f(x)的最大值为f(1)=1;
3、 当x∈[0,1/2]时,由f(x1+x2)≥f(x1)+f(x2),令x1=x2=x,得证.
当x∈(1/2,1]时,∵ f(x)的最大值为f(1)=1;
∴f(x)≤1<2X
题有问题,定义域为[0,1]但是第二行出现了f(x1)+f(2)求解时……