We know that the positive scale function y = 4x and the inverse scale function y = KX. (1) what is the value of K? When k is a value, there is no intersection between the two functions? (2) Can there be only one intersection of the two functions? If yes, find out the coordinates of the intersection point; if not, explain the reason

We know that the positive scale function y = 4x and the inverse scale function y = KX. (1) what is the value of K? When k is a value, there is no intersection between the two functions? (2) Can there be only one intersection of the two functions? If yes, find out the coordinates of the intersection point; if not, explain the reason

(1) The simultaneous analytic formula: y = 4xy = KX, we can get: 4x = KX, ∵ x ≠ 0, ∵ x2 = K4, if the image of two functions has two intersections, then K4 > 0, the solution is: K > 0; if the image of two functions has no intersection, then K4 < 0, the solution is: K < 0. (2) ∵ K ≠ 0, the image of two functions cannot have only one intersection