Solution: (1) Let any two points on the image and the function y=f(x) P 1(x 1, y 1), P2(x2, y2),

Let's set x 1 > x2,

Then (y 1? y2)/(x 1？ X2) < 1, that is [? x 1^3+ax 1^2+x 2^3？ Axe 2 2]/[x1? x2]< 1，

∴[? (x 1？ x2)(x 1^ 2+x 1x 2+x 2^2)+a(x 1？ x2)(x 1+x2)]/[x 1？ x2]< 1

Ordered: x12+(x2-a) x1+x2-ax2+1> 0.

∫x 1∈R

∴△ = (x2-a) 2-4 (x2-ax2+1) < 0 means 3x2 2-2ax2-a 2+4 > 0.

∫x2∈R

∴△ = 4a 2- 12 (-a 2+4) < 0 means a 2-3 < 0.

∴-root number 3 < a