If the inverse function image of y = (A-X) / (x-a-1) is centrosymmetric with respect to the point (- 1,4), then the value of a is? The answer is that a is 3 What should we do

If the inverse function image of y = (A-X) / (x-a-1) is centrosymmetric with respect to the point (- 1,4), then the value of a is? The answer is that a is 3 What should we do

"The inverse function image is centrosymmetric with respect to the point (- 1,4)", so "the inverse function image is centrosymmetric with respect to the point (4, - 1)"
Translate the function to the left by 4 units, and then up by 1 unit: Y - 1 = (a - X - 4) / (x - A + 3), at this time, the center of symmetry becomes (0, 0), and the function passes through (a, - 1 / 3), so it should also pass through its symmetric point (- A, 1 / 3) about (0,0), substituting to get: a = 3