If a function is symmetric with respect to a point, is its inverse symmetric with respect to that point

If a function is symmetric with respect to a point, is its inverse symmetric with respect to that point

For example, any point of the straight line y = x + 1 can be regarded as its center of symmetry. It can not be said that its inverse function y = X-1 is also symmetrical about any point of the straight line y = x + 1