2. when m>0 and x≤0, g(x) is not positive, so it must be f(x)>0 and x≤0.

The symmetry axis of f (x) is x=m/4- 1.

When m ≥ 4, the minimum value of f(x) at (-∞, 0] f(0)=4-m≤0 does not satisfy the condition.

The minimum value of 0<m<4 and f(x) on (-∞, 0] f(m/4- 1)=2-m? /8 & gt； 0, qualified

3. When M

The symmetry axis of f (x) is x = m/4- 1

∴m<； 0, the minimum value of f(x) at [0, +∞] f (0) = 4-m >; 0, qualified

To sum up, the value range of m is (-∞, 4).