Firstly, that's an odd use of the term 'reverse' when talking about mathematical functions. At any rate, your table of values doesn't even follow from your definition of the function F.
To get F(-1) = 0, I presume you decided to 'invert' the operator, which would make F(-2) = (-2) ÷ [(-2) - (-2)] = -2 ÷ 0, which is undefined (not infinity). Since all subsequent terms will end with a (-x) - (-x) in a denominator, they are ALL undefined.
That being said, I think you have the beginning of an intriguing idea: the *down* arrow for repeated division.