(1)∫ The image of inverse proportional function y = kx passes through point A (1, 2),

Then xy=2,

∴k=2，

∴ The analytical formula of inverse proportional function is: y = 2x.

(2) the point B(m, n) is on the image of y = 2x,

∴ n = 2m, namely mn=2,

∫s△ABC = 12m(2？ n)= 12m(2？ 2m)=m？ 1=2,

∴m=3，

∴n=2m=23

∴B's coordinate is (3,23);

(3) Substitute A (1, 2) and B (3, 23) into y=ax- 1 respectively to obtain:

a 1=3，a2=59

So the range of a is 59 < a < 3.