Let the straight line passing through the origin (0,0) and f(x) be tangent to the point (t, et).

Then the slope of the tangent is e t/t.

F' (x) = e x, then the slope of the tangent is f' (t) = e t.

Therefore, e t/t = e t, that is, t= 1, the tangent point is (1, e), and the tangent slope is e.

The tangent equation is y=e(x- 1)+e, that is, y=ex.

If the equation e x-ax = 0 has a unique solution about X, then the curve y = e x and the straight line y=ax have a unique intersection.

So the range of a is (-infinity, 0)U[e,+infinity).