函数f(x)=x+|x-2c|-1在R上恒为正值的充要条件是

2025-06-22 12:39:11
推荐回答(1个)
回答1:

当x<=2c时,f(x) = x + 2c-x -1 = 2c-1 > 0 =>c > 1/2
当x > 2c时,f(x) = x + x -2c -1 = 2x-2c-1>0 => x > c+1/2
即x > 2c时 x > c+1/2 所以 2c>c+1/2 => c>1/2
反之,当c >1/2时, 可推出f(x) > 0
故充要条件为 c>1/2