设函数f（x）的定义域为R,若存在常数m＞0,使|f（x）|

1.是,取 m =1 即可.
2.是,取 m =2 即可.
3.不是,f(x) = √2( sinx+cosx) = 2 sin(x+π/4)
当x=0时,有 f(0) = √2 ,不能满足 |f(0)| ≤ m |x|.
4.x²+x+1 = (x+1/2)²+3/4 ≥ 3/4
|f(x)| ≤ (4/3) |x| ,取 m=4/3 即可.