Why does InverseFunction [0 &] @ 0 return 33/10?

Question

In Mathematica 8.0.1.0 on 32-bit Linux expression

InverseFunction[0 &]@0 

returns 33/10 . (The same thing happens for other integer and rational values, I use 0 as an example.)

According to the documentation for InverseFunction :

As discussed in functions that do not have unique values, many mathematical functions do not have unique inversions. In such cases, InverseFunction [f] can represent only one of the possible inverse for f.

As a constant function 0& returns 0 regardless of its input, it has infinitely many inverse functions (each of which is defined only in 0). So, as defined, this answer is within the specification.

Secret: why does it give 33/10 , and not any other meaning ?

Answer 1

This number appears in multiple copies. Take for example:

FindInstance [x == x, x, Reals]

{{x> 33/10}}

I saw how this number was discussed. This is basically just the result of using Mathematica. You will get this sometimes when you ask Mathematica to do something that boils down to "Choosing a Random Real Number." It does not really matter.