As shown in the figure, it is known that the image with positive scale function y = 3 / 4x and the image with inverse scale function y = K / X intersect at point a, and make a straight line ab ‖ Y axis through point a, and intersect X axis at point B, OB = 4 , m (m, n) is a moving point on the inverse scale function image, where 0 < n < 4 (1) The expression of inverse proportion function (2) When om = OA, find the value of M + n (3) Make a straight line MC ∥ X axis through point m, intersect Y axis with point C, intersect a straight line AB at point D. when the area of quad OADM is 12, please judge the size relationship between cm and DM, and explain the reason

(1) Let the coordinates of point a (x, y) be x = 4
Since point a is on the line y = 3 / 4x, we get y = 3, that is, a (4,3)
Because if the inverse scale function image passes through point a, then 3 = K / 3, then k = 9
So the inverse scale function y = 9 / X
(2) Because △ AOB is a right triangle, and ob = 4, ab = 3, angle oba = 90 °, then OA = 5
When om = OA = 5, M & # 178; + n & # 178; = om & # 178; = 25
Because m point is on the inverse proportion function, it satisfies n = 9 / M (0 < n < 4) 2
If (M + n) ² = M & #178; + n & #178; + 2Mn = 43, then M + n = radical 43
(3) The coordinate of point d (4, n) can be obtained from the meaning of the title
The area s of quad OADM is the sum of the areas of △ OAD and △ ADM, that is s = s △ oad + s △ ADM = 1 / 2 * ob * ad + 1 / 2 * DM * ad = 12
That is, 4 * | n-3 | + | M-4 | * | n-3 | = 24
（4+|m-4|）*|n-3|=24 ③
When 0 ＜ m ≤ 4, there is (8-m) * | n-3 | = 24
In this case, 4 ≤ 8-m < 8
If ∵ 0 | n | 4, then 0 | n-3 | 3, then (4) is impossible
So m > 4
So D is between M and C
Cm = CD + DM > DM

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