When x≤ 1, f(x)=x? -4x+ 1 is a quadratic function with the symmetry axis x=2. According to its image, it monotonically decreases in (-∞, 1).

When x> is at 1, f(x)=ax+2 is a linear function. If the whole function is required to decrease monotonically within (-∞, +∞), it must be x >；; At 1, f(x)=ax+2 also decreases monotonically, therefore, (1): a.

At the same time, it is required that the whole function monotonically decreases in (-∞,+∞), and when x >; At 1, the image with f(x)=ax+2 is at f(x)=x? -4x+ 1(x≤ 1), that is, f (x) = ax+2 (x > The maximum ratio of 1) is f(x)=x? The minimum value of -4x+ 1(x≤ 1) is small.

And f (x) = ax+2 (x >; 1) monotonically decreases, so f (x) = ax+2 (x >; 1) is a+2 (that is, when x= 1).

f(x)=x？ -4x+ 1(x≤ 1) also monotonically decreases, so f(x)=x? The minimum value of -4x+ 1(x≤ 1) is -2 (that is, when x= 1).

Therefore, a+2 < -2, that is, (2): a.

The key of this topic is f (x) = ax+2 (x >; 1) is a hollow ray. When its "maximum" (actually there is no maximum) a+2=-2, f(x) is a closed curve at (-∞,+∞), so: (3)a can also be equal to -4.

Comprehensive (1), (2) and (3), a≤-4.