f(x)=[(3a+2)x+1]/(x-2a). If the image of the inverse function of F (x) coincides with the image of y = f (x), find a Another: why is the symmetry center of y = f (x) image (2a, 3A + 2)? How to find the center of symmetry of a function?

f(x)=[(3a+2)x+1]/(x-2a). If the image of the inverse function of F (x) coincides with the image of y = f (x), find a Another: why is the symmetry center of y = f (x) image (2a, 3A + 2)? How to find the center of symmetry of a function?

Let y = [(3a + 2) x + 1] / (x-2a)
Then x = (2ay + 1) / [y - (3a + 2)]
So let y = = (2aX + 1) / [x - (3a + 2)]
If the two equations are equal, a = - 2
Symmetry center solving method: first give a definition: if the function f (x) satisfies f (x) + F (2a-x) = 2B, then (a, b) is its symmetry center. You can verify it by bringing it in